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Recent questions and answers in Linear Algebra
+15
votes
5
answers
1
GATE2005IT3
The determinant of the matrix given below is $\begin{bmatrix} 0 &1 &0 &2 \\ 1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& 2& 0& 1 \end{bmatrix}$ $1$ $0$ $1$ $2$
answered
Aug 5
in
Linear Algebra
by
Satbir
Boss
(
17.2k
points)

1.8k
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gate2005it
linearalgebra
normal
determinant
+9
votes
3
answers
2
GATE20021.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
answered
Jul 31
in
Linear Algebra
by
thambu
(
11
points)

831
views
gate2002
linearalgebra
easy
matrices
0
votes
1
answer
3
MADE EASY
The Necessary condition to diagonalize a matrix is that A) ITS all eigen values should be distdist B) its eigen vectors should be indeindepent C) its eigen values should be real D) matrix is non singular
answered
Jul 30
in
Linear Algebra
by
Jyotish Ranjan
(
11
points)

51
views
+41
votes
7
answers
4
GATE2014247
The product of the nonzero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
answered
Jul 24
in
Linear Algebra
by
srestha
Veteran
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113k
points)

9.4k
views
gate20142
linearalgebra
eigenvalue
normal
numericalanswers
+1
vote
1
answer
5
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
Jun 21
in
Linear Algebra
by
suraj
Loyal
(
6k
points)

295
views
gate1998
linearalgebra
systemofequations
descriptive
+37
votes
3
answers
6
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
Jun 15
in
Linear Algebra
by
Ashwani Kumar 2
Boss
(
14.8k
points)

3k
views
gate2007
eigenvalue
linearalgebra
difficult
+2
votes
2
answers
7
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
in
Linear Algebra
by
ankitgupta.1729
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14k
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277
views
gate1988
normal
descriptive
linearalgebra
matrices
0
votes
1
answer
8
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
in
Linear Algebra
by
Sourajit25
Junior
(
997
points)

75
views
linearalgebra
+17
votes
4
answers
9
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
in
Linear Algebra
by
ankitgupta.1729
Boss
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14k
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3.1k
views
gate2007
linearalgebra
normal
vectorspace
0
votes
1
answer
10
GATE 2019:EC
The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________
answered
Jun 3
in
Linear Algebra
by
srestha
Veteran
(
113k
points)

65
views
discretemathematics
+1
vote
4
answers
11
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
in
Linear Algebra
by
Debargha Bhattacharj
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(
515
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151
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discretemathematics
matrix
+21
votes
3
answers
12
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
in
Linear Algebra
by
ankitgupta.1729
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14k
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2.7k
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gate20151
linearalgebra
matrices
numericalanswers
0
votes
2
answers
13
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
in
Linear Algebra
by
Satbir
Boss
(
17.2k
points)

105
views
discretemathematics
linearalgebra
matrix
matrices
+1
vote
1
answer
14
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
Junior
(
565
points)

79
views
tifrmaths2014
linearalgebra
matrices
0
votes
1
answer
15
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
(
233
points)

120
views
engineeringmathematics
linearalgebra
matrices
+17
votes
3
answers
16
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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1.7k
points)

2.9k
views
gate2003
linearalgebra
systemofequations
normal
0
votes
0
answers
17
GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
[closed]
asked
May 28
in
Linear Algebra
by
Hirak
Active
(
3.4k
points)

58
views
eigenvalue
linearalgebra
+8
votes
1
answer
18
Mathematics 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
(
39
points)

531
views
engineeringmathematics
gate2015ee
+17
votes
3
answers
19
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
in
Linear Algebra
by
MRINMOY_HALDER
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1.7k
points)

2.4k
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gate2012
linearalgebra
eigenvalue
0
votes
2
answers
20
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
Boss
(
34.4k
points)

79
views
engineeringmathematics
linearalgebra
+1
vote
1
answer
21
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)

59
views
isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
0
votes
1
answer
22
#GATE 2014 IN
answered
May 14
in
Linear Algebra
by
Satbir
Boss
(
17.2k
points)

30
views
0
votes
1
answer
23
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
Loyal
(
7k
points)

51
views
isi2018
engineeringmathematics
linearalgebra
determinant
0
votes
2
answers
24
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
Veteran
(
113k
points)

74
views
isi2018
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
answer
25
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
by
Verma Ashish
Loyal
(
9.1k
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59
views
isi2018
engineeringmathematics
linearalgebra
eigenvalue
determinant
0
votes
2
answers
26
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 $8$ $10$ $12$ $14$
answered
May 9
in
Linear Algebra
by
pratekag
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(
2k
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180
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isi2019
engineeringmathematics
linearalgebra
+1
vote
1
answer
27
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
answered
May 7
in
Linear Algebra
by
pratekag
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(
2k
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120
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isi2019
engineeringmathematics
linearalgebra
0
votes
2
answers
28
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
in
Linear Algebra
by
Shikha Mallick
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3.4k
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152
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isi2019
linearalgebra
engineeringmathematics
+1
vote
1
answer
29
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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1.7k
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123
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isi2019
linearalgebra
systemofequations
+10
votes
4
answers
30
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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659
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gate1996
linearalgebra
matrices
normal
descriptive
+1
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0
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31
CSIR UGC NET
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Apr 28
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41
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linearalgebra
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0
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32
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..!
asked
Apr 27
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Linear Algebra
by
Hirak
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50
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33
Virtual Gate Test Series: Linear Algebra  Rank Of The Matrix
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Apr 27
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virtualgatetestseries
+3
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1
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34
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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+3
votes
4
answers
35
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
in
Linear Algebra
by
gaurav1.yuva
(
437
points)

1.8k
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gate2019
engineeringmathematics
linearalgebra
determinant
+2
votes
1
answer
36
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
in
Linear Algebra
by
Sushantkala786
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11
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79
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tifrmaths2015
linearalgebra
0
votes
4
answers
37
ISRO 2012 ECE Matrices
The Eigen values of matrix are: a) ± cos∝ b) ± sin ∝ c) tan ∝ & cot ∝ d) cos ∝ ± sin ∝
answered
Mar 10
in
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by
Debdeep1998
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engineeringmathematics
isroece
isro2012ece
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eigenvalue
0
votes
3
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38
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
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linearalgebra
+4
votes
4
answers
39
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
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9.1k
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255
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0
votes
1
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40
Ace Test Series: Linear Algebra  Eigen Values
answered
Mar 9
in
Linear Algebra
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34.4k
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160
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