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Recent questions and answers in Linear Algebra
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1
GATE19989
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one operation refers to a multiplication followed by an addition.
answered
4 hours
ago
in
Linear Algebra
by
Arjun
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406k
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259
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gate1998
linearalgebra
systemofequations
gaussianelimination
descriptive
+37
votes
3
answers
2
GATE200725
Let A be a $4 \times 4$ matrix with eigen values 5,2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $5$ $7$ $2$ $1$
answered
2 days
ago
in
Linear Algebra
by
Ashwani Kumar 2
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14.6k
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2.9k
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gate2007
eigenvalue
linearalgebra
difficult
+2
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2
answers
3
GATE198816i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lowertriangular with all diagonal elements equal to 1, $U$ is uppertriangular, and $P$ is a permutation matrix. For $A = \begin{bmatrix} 2 & 5 & 9 \\ 4 & 6 & 5 \\ 8 & 2 & 3 \end{bmatrix}$ Compute $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
answered
Jun 8
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Linear Algebra
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ankitgupta.1729
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252
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gate1988
normal
descriptive
linearalgebra
matrices
0
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1
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4
Linear Algebra (Self Doubt)
Let $A$ be a $n \times n$ square matrix whose all columns are independent. Is $Ax = b$ always solvable? Actually, I know that $Ax= b$ is solvable if $b$ is in the column space of $A$. However, I am not sure if it is solvable for all values of $b$.
answered
Jun 7
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Linear Algebra
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Sourajit25
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953
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linearalgebra
+17
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4
answers
5
GATE200727
Consider the set of (column) vectors defined by $X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$ ... a linearly independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above
answered
Jun 6
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Linear Algebra
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ankitgupta.1729
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gate2007
linearalgebra
normal
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1
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6
GATE 2019:EC
The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________
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Jun 3
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Linear Algebra
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srestha
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111k
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54
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discretemathematics
+1
vote
4
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7
GATE2017 EC
The rank of the matrix $\begin{bmatrix} 1 & 1 & 0 &0 & 0\\ 0 & 0 & 1 &1 &0 \\ 0 &1 &1 &0 &0 \\ 1 & 0 &0 & 0 &1 \\ 0&0 & 0 & 1 & 1 \end{bmatrix}$ is ________. Ans 5?
answered
Jun 3
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Linear Algebra
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Debargha Bhattacharj
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349
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88
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discretemathematics
matrix
+21
votes
3
answers
8
GATE2015118
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ of $L$ is_________________.
answered
Jun 2
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Linear Algebra
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ankitgupta.1729
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gate20151
linearalgebra
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numericalanswers
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2
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9
GATE 2017:EC
Consider the $5\times 5$ matrix: $\begin{bmatrix} 1 & 2 &3 & 4 &5 \\ 5 &1 &2 & 3 &4 \\ 4& 5 &1 &2 &3 \\ 3& 4 & 5 & 1 &2 \\ 2&3 & 4 & 5 & 1 \end{bmatrix}$ It is given $A$ has only one real eigen value. Then the real eigen value of $A$ is ________
[closed]
answered
Jun 2
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Linear Algebra
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Satbir
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58
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discretemathematics
linearalgebra
matrix
matrices
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1
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10
TIFR2014MathsA11
Let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$ (0matrix), for some $k \in \mathbb{N}$. Then $A$ has to be the $0$ matrix Trace$(A)$ could be nonzero $A$ is diagonalizable $0$ is the only eigenvalue of $A$.
answered
May 31
in
Linear Algebra
by
Yash4444
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467
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78
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tifrmaths2014
linearalgebra
matrices
0
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1
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11
SelfDoubt: Diagonalizable Matrix
$1)$ How to find a matrix is diagonalizable or not? Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & \cos\Theta \end{bmatrix}$ Is it diagonalizable? $2)$ What is it’s eigen spaces?
answered
May 30
in
Linear Algebra
by
lolster
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223
points)

106
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engineeringmathematics
linearalgebra
matrices
+17
votes
3
answers
12
GATE200341
Consider the following system of linear equations ... are linearly dependent. For how many values of $\alpha$, does this system of equations have infinitely many solutions? \(0\) \(1\) \(2\) \(3\)
answered
May 29
in
Linear Algebra
by
MRINMOY_HALDER
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gate2003
linearalgebra
systemofequations
normal
0
votes
0
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13
GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
[closed]
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May 28
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Linear Algebra
by
Hirak
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3k
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48
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eigenvalue
linearalgebra
+8
votes
1
answer
14
GATE EE
The maximum value of a such that the matrix below has three linearly independent real eigen vectors is $\begin{pmatrix} 3& 0 &2 \\ 1& 1 & 0\\ 0& a & 2 \end{pmatrix}$ (a) $\frac{2}{3\sqrt{3}}$ (b) $\frac{1}{3\sqrt{3}}$ (c) $\frac{1+2\sqrt{3}}{3\sqrt{3}}$ (d)$\frac{1+\sqrt{3}}{3\sqrt{3}}$
answered
May 27
in
Linear Algebra
by
Aishvarya Akshaya Vi
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39
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508
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engineeringmathematics
gate2015ee
+17
votes
3
answers
15
GATE201211
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$
answered
May 27
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MRINMOY_HALDER
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gate2012
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0
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2
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16
Engineering Maths
If A = $\begin{bmatrix} 1 & 1 & 0 \\ 0 & 2 &2 \\ 0& 0 & 3 \end{bmatrix}$ then trace of the matrix 3A2 + adj A is ____
answered
May 26
in
Linear Algebra
by
abhishekmehta4u
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engineeringmathematics
linearalgebra
+1
vote
1
answer
17
ISI2018PCBA1
Consider a $n \times n$ matrix $A=I_n\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
answered
May 20
in
Linear Algebra
by
Kaustubh Vande
(
11
points)

54
views
isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
0
votes
1
answer
18
#GATE 2014 IN
answered
May 14
in
Linear Algebra
by
Satbir
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12.9k
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28
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0
votes
1
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19
ISI2018MMA13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
answered
May 12
in
Linear Algebra
by
Sayan Bose
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6.9k
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42
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isi2018
engineeringmathematics
linearalgebra
determinant
0
votes
2
answers
20
ISI2018MMA12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
answered
May 11
in
Linear Algebra
by
srestha
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(
111k
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65
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isi2018
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
answer
21
ISI2018MMA14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $4$ $2$ $2$ $4$
answered
May 11
in
Linear Algebra
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Verma Ashish
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53
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isi2018
engineeringmathematics
linearalgebra
eigenvalue
determinant
0
votes
2
answers
22
ISI2019MMA13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$
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May 9
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Linear Algebra
by
pratekag
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isi2019
engineeringmathematics
linearalgebra
0
votes
1
answer
23
ISI2019MMA23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skewsymmetric matrix None of the above must necessarily hold
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May 7
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Linear Algebra
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pratekag
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113
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isi2019
engineeringmathematics
linearalgebra
0
votes
2
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24
ISI2019MMA15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & 1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$
answered
May 7
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Linear Algebra
by
Shikha Mallick
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145
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isi2019
linearalgebra
engineeringmathematics
0
votes
1
answer
25
ISI2019MMA14
If the system of equations $\begin{array} ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1a} + \frac{1}{1b} + \frac{1}{1c}$ is $1$ $1$ $3$ $3$
answered
May 7
in
Linear Algebra
by
MRINMOY_HALDER
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isi2019
linearalgebra
systemofequations
+10
votes
4
answers
26
GATE199610
Let $A = \begin{bmatrix} a_{11} && a_{12} \\ a_{21} && a_{22} \end{bmatrix} \text { and } B = \begin{bmatrix} b_{11} && b_{12} \\ b_{21} && b_{22} \end{bmatrix}$ be two matrices such that $AB=I$. Let $C = A \begin{bmatrix} 1 && 0 \\ 1 && 1 \end{bmatrix}$ and $CD =I$. Express the elements of $D$ in terms of the elements of $B$.
answered
May 3
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Linear Algebra
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MRINMOY_HALDER
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gate1996
linearalgebra
matrices
normal
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0
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27
CSIR UGC NET
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Apr 28
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Hirak
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36
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liner
linearalgebra
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matrixinversion
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0
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28
Made Easy Engineering Maths book
The ans given is b, but i am not able to understande why. According to me the largest eigen value is 2, and therefore none of the option matches..!
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Apr 27
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Linear Algebra
by
Hirak
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50
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+1
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2
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29
Virtual Gate Test Series: Linear Algebra  Rank Of The Matrix
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Apr 27
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Linear Algebra
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SuvasishDutta
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655
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engineeringmathematics
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matrix
rankofmatrix
virtualgatetestseries
+3
votes
1
answer
30
Vani Institute Question Bank Pg231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $a,2a,2a$ $a,a+\sqrt{2},a\sqrt{2}$
answered
Apr 27
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Linear Algebra
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SuvasishDutta
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655
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85
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engineeringmathematics
linearalgebra
eigenvalue
+3
votes
4
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31
GATE20199
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is nonzero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
answered
Apr 23
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Linear Algebra
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gaurav1.yuva
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427
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1.7k
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gate2019
engineeringmathematics
linearalgebra
determinant
+2
votes
1
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32
TIFR2015MathsB13
Let $X=\left\{(x, y) \in \mathbb{R}^{2}: 2x^{2}+3y^{2}= 1\right\}$. Endow $\mathbb{R}^{2}$ with the discrete topology, and $X$ with the subspace topology. Then. $X$ is a compact subset of $\mathbb{R}^{2}$ in this topology. $X$ is a connected subset of $\mathbb{R}^{2}$ in this topology. $X$ is an open subset of $\mathbb{R}^{2}$ in this topology. None of the above.
answered
Apr 8
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Linear Algebra
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Sushantkala786
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11
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77
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tifrmaths2015
linearalgebra
0
votes
4
answers
33
ISRO 2012 ECE Matrices
The Eigen values of matrix are: a) ± cos∝ b) ± sin ∝ c) tan ∝ & cot ∝ d) cos ∝ ± sin ∝
answered
Mar 10
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Debdeep1998
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isroece
isro2012ece
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0
votes
3
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34
ISRO2012ECE: Engineering Mathematics
The system of equations x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8 has a. A unique solution b. No solution c. An infinite number of solutions d. None of these
answered
Mar 10
in
Linear Algebra
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isro2012ece
isroece
engineeringmathematics
linearalgebra
+4
votes
4
answers
35
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
answered
Mar 10
in
Linear Algebra
by
Verma Ashish
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7.3k
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240
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matrices
eigenvalue
0
votes
1
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36
Ace Test Series: Linear Algebra  Eigen Values
answered
Mar 9
in
Linear Algebra
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abhishekmehta4u
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33.9k
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155
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engineeringmathematics
linearalgebra
eigenvalue
0
votes
2
answers
37
ISRO 2014 Trigonometry [EE]
If tan $\Theta$ = 8 / 15 and $\Theta$ is acute, then cosec $\Theta$ (A) 8 / 17 (B) 8 / 15 (C) 17 / 8 (D) 17 / 15
answered
Mar 7
in
Linear Algebra
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abhishekmehta4u
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207
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isroee
engineeringmathematics
0
votes
0
answers
38
ISIMMA201544
Let $P_{1},P_{2},$ and $P_{3}$ denote, respectively, the planes defined by $a_{1}x + b_{1}y + c_{1}z = \alpha _{1}$ $a_{2}x + b_{2}y + c_{2}z = \alpha _{2}$ $a_{3}x + b_{3}y + c_{3}z = \alpha _{3}$ It is given ... then the planes (A) do not have any common point of intersection (B) intersect at a unique point (C) intersect along a straight line (D) intersect along a plane
asked
Feb 22
in
Linear Algebra
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ankitgupta.1729
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13.2k
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81
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engineeringmathematics
linearalgebra
userisi2015
usermod
0
votes
1
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39
Linear AlgebraMETest
If the determinant of the below matrix is 245, what is the value of X? $\begin{bmatrix} 0 & 4& 2 &1 \\ 3& 1 & 0 & 2\\ 5&2 & x& 4\\ 6& 1 & 1 & 0 \end{bmatrix}$ ... , because by keeping 6 in place of x I am getting determinant as 245(Result verified by computer program). Please let me know where I am going wrong?
answered
Feb 19
in
Linear Algebra
by
Meet2698
(
195
points)

140
views
linearalgebra
engineeringmathematics
+20
votes
4
answers
40
GATE2015227
Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$ Add the third row to the second row Subtract the third column from the first column. The determinant of the resultant matrix is _____.
answered
Feb 18
in
Linear Algebra
by
Ram Swaroop
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gate20152
linearalgebra
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numericalanswers
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