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Recent questions and answers in Linear Algebra
+11
votes
6
answers
1
GATE20011.1
Consider the following statements: S1: The sum of two singular $n \times n$ matrices may be nonsingular S2: The sum of two $n \times n$ nonsingular matrices may be singular Which one of the following statements is correct? $S1$ and $S2$ both are true $S1$ is true, $S2$ is false $S1$ is false, $S2$ is true $S1$ and $S2$ both are false
answered
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Linear Algebra
by
Prince Sindhiya
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gate2001
linearalgebra
normal
matrices
+13
votes
4
answers
2
GATE200426
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2  n\right)}{2}\right)$
answered
5 days
ago
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Linear Algebra
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janeb abhishek
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291
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2.1k
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gate2004
linearalgebra
normal
matrices
+20
votes
4
answers
3
GATE200623
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows
answered
5 days
ago
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Linear Algebra
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janeb abhishek
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291
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1.3k
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gate2006
linearalgebra
normal
matrices
+1
vote
2
answers
4
mathematics
Consider the set H of all 3 × 3 matrices of the type where a, b, c, d, e and f are real numbers and abc ≠ 0. Under the matrix multiplication operation, the set H is a group a monoid but not a group C a semigroup but not a monoid D neither a group nor a semigroup
answered
Jun 13
in
Linear Algebra
by
talha hashim
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803
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87
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engineeringmathematics
+1
vote
0
answers
5
Engineering Maths: Orthogonal Matrix
Is the given last point correct? But as i see in the given matrix sum of the product of first two columns (or) two rows is not zero. please verify.
asked
Jun 13
in
Linear Algebra
by
pbhati
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35
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11
views
linearalgebra
engineeringmathematics
0
votes
0
answers
6
Matrix multiplication Gilbert strang
Multiple Interpretations of Matrix Multiplications Say we are multiplying two matices A B = C. Multiple ways to interpret this operation: Rowwise approach: Ci = Ai B. Rows of C are linear combinations of rows in B Column multiplied by rows: ... of A and ith row of B! I am unable to understand these two ways as mentioned in gibert strang book and video ?
asked
Jun 2
in
Linear Algebra
by
Sandy Sharma
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437
points)

36
views
0
votes
0
answers
7
Gilbert Strang  Real Symmetric Matrices
asked
Jun 2
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Linear Algebra
by
ankitgupta.1729
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6.1k
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34
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linearalgebra
gilbertstrang
matrix
engineeringmathematics
+3
votes
3
answers
8
ISRODEC20171
Suppose $A$ is a finite set with $n$ elements.The number of elements and the rank of the largest equivalence relation on $A$ are $\{n,1\}$ $\{n,n\}$ $\{n^2,1\}$ $\{1,n^2\}$
answered
May 31
in
Linear Algebra
by
Sahreen
(
23
points)

2.3k
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isrodec2017
0
votes
2
answers
9
Made easy test
Consider the rank of matrix $'A'$ of size $(m \times n)$ is $"m1"$. Then, which of the following is true? $AA^T$ will be invertible. $A$ have $"m1"$ linearly independent rows and $"m1"$ linearly ... and $"n"$ linearly independent columns. $A$ will have $"m1"$ linearly independent rows and $"n1"$ independent columns.
answered
May 31
in
Linear Algebra
by
srestha
Veteran
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86.9k
points)

70
views
engineeringmathematics
linearalgebra
matrices
0
votes
1
answer
10
Made easy test
Which of the following matrices is LU DECOMPOSIBLE? How to find it? $\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 1 & 3 & 4 \end{bmatrix}$ $\begin{bmatrix} 3 & 2 \\ 0 & 1 \end{bmatrix}$ $\begin{bmatrix} 0 & 1 \\ 3 & 2 \end{bmatrix}$ $\begin{bmatrix} 1 & 3 & 7 \\ 2 & 6 & 1 \\ 0 & 3 & 2 \end{bmatrix}$
answered
May 31
in
Linear Algebra
by
Kushagra Chatterjee
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8.2k
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56
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engineeringmathematics
linearalgebra
+1
vote
1
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11
Matrix
Each row of M can be represented as a linear combination of the other rows 1)Does that mean linear combination of other rows will be 0? how ? 2)And also , is linear combination means add, subtract, multiply and divide , but not squaring or root or exponential operation,right? https://gateoverflow.in/3319/gate2008it29
answered
May 31
in
Linear Algebra
by
Kushagra Chatterjee
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8.2k
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68
views
linearalgebra
matrices
engineeringmathematics
0
votes
1
answer
12
If A and B are matrices of order 4 x 4 such that A= 5B and determinant of A = X. (determinant of B), then X will be
answered
May 30
in
Linear Algebra
by
Prateek Raghuvanshi
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3.9k
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45
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engineeringmathematics
linearalgebra
+27
votes
3
answers
13
GATE2017131
Let $A$ be $n\times n$ real valued square symmetric matrix of rank 2 with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} =$ 50. Consider the following statements. One eigenvalue must be in $\left [ 5,5 \right ]$ The eigenvalue with the largest ... greater than 5 Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II
answered
May 29
in
Linear Algebra
by
Prateek Raghuvanshi
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3.4k
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gate20171
linearalgebra
eigenvalue
normal
+1
vote
3
answers
14
Matrix
The matrix $A=\begin{bmatrix} 1 &4 \\ 2 &3 \end{bmatrix}$ satisfies the following polynomial $A^{5}4A^{4}7A^{3}+11A^{2}2A+kI=0$ Then the value of k is ______________
answered
May 27
in
Linear Algebra
by
Subarna Das
Boss
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10.7k
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165
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linearalgebra
matrices
engineeringmathematics
0
votes
0
answers
15
related to previous year
can someone verify my answer given to this matrices question ? https://gateoverflow.in/3319/gate2008it29
asked
May 20
in
Linear Algebra
by
mehul vaidya
Junior
(
993
points)

34
views
0
votes
2
answers
16
ISRODEC201710
If vectors $\vec{a}=2\hat{i}+\lambda \hat{j}+\hat{k}$ and $\vec{b}=\hat{i}2\hat{j}+3\hat{k}$ are perpendicular to each other, then value of $\lambda$ is $\dfrac{2}{5}$ $2$ $3$ $\dfrac{5}{2}$
answered
May 19
in
Linear Algebra
by
Mk Utkarsh
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(
12.6k
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726
views
isrodec2017
vectorspace
0
votes
0
answers
17
Vector
https://www.youtube.com/watch?v=3SkCNpFOshk In this lecture , can somebody define in 2nd question why $X_{1}+X_{2}\notin V_{1}\cup V_{2}$? I cannot understand the proof
asked
May 17
in
Linear Algebra
by
srestha
Veteran
(
86.9k
points)

26
views
vectorspace
engineeringmathematics
0
votes
1
answer
18
ISI 2018 MMA 2
The volume of the region $S=\{(x,y,z) :\left  x \right +\left  y \right +\left  z \right \leq 1\}$ is $\frac{1}{6}$ $\frac{1}{3}$ $\frac{2}{3}$ $\frac{4}{3}$
answered
May 14
in
Linear Algebra
by
Kushagra Chatterjee
Loyal
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8.2k
points)

69
views
isi2018
vectorspace
+18
votes
5
answers
19
GATE201424
If the matrix $A$ is such that $$A= \begin{bmatrix} 2\\ −4\\7\end{bmatrix}\begin{bmatrix}1& 9& 5\end{bmatrix}$$ then the determinant of $A$ is equal to ______.
answered
May 14
in
Linear Algebra
by
srestha
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(
86.9k
points)

1.3k
views
gate20142
linearalgebra
numericalanswers
easy
determinant
0
votes
0
answers
20
Matrix
To find the product of the nonzero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 ... [ \left ( 1\lambda \right )\left ( \lambda ^{2}2\lambda \right ) \right ]$ then $\lambda =1,2,0$ Where is my mistake, plz tell me
asked
May 14
in
Linear Algebra
by
srestha
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86.9k
points)

148
views
linearalgebra
matrices
engineeringmathematics
+1
vote
1
answer
21
Identify Lattice
Which of these diagrams are lattice and why?
answered
May 7
in
Linear Algebra
by
Deepakk Poonia (Dee)
Boss
(
13.2k
points)

107
views
lattice
discretemathematics
+2
votes
1
answer
22
Lattice
Lattice or not and why?
answered
May 7
in
Linear Algebra
by
Deepakk Poonia (Dee)
Boss
(
13.2k
points)

115
views
lattice
discretemathematics
+21
votes
3
answers
23
GATE201713
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ where $A=\left [ a_{1}.....a_{n} \ ... of equations has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$dimensional vector of all 1. no solution infinitely many solutions finitely many solutions
answered
May 6
in
Linear Algebra
by
srestha
Veteran
(
86.9k
points)

3.2k
views
gate20171
linearalgebra
systemofequations
normal
+10
votes
3
answers
24
GATE201826
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the following options ... and III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
answered
May 6
in
Linear Algebra
by
Ayush Upadhyaya
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(
9k
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1.8k
views
gate2018
linearalgebra
matrices
eigenvalue
normal
0
votes
2
answers
25
GATE 2016 EE SET 1
Let the eigenvalues of 2 x 2 matrix A be 1, 2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2  3A+4I would respectively, be (a) 2,14; x1,x2 (b) 2,14; x1+x2:x1x2 (c) 2,0; x1, x2 (d) 2,0; x1+x2,x1x2
answered
May 2
in
Linear Algebra
by
Kushagra Chatterjee
Loyal
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8.2k
points)

85
views
linearalgebra
gate2016ee2
eigenvalue
+18
votes
2
answers
26
GATE2008IT29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the ... : $MX = 0$ has a nontrivial solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$
answered
Apr 29
in
Linear Algebra
by
mehul vaidya
Junior
(
993
points)

1.1k
views
gate2008it
linearalgebra
normal
matrices
0
votes
3
answers
27
gilbert strang Problem Set 2.1
Which of the following descriptions are correct? The solutions x of Ax = $\begin{bmatrix} 1 & 1 & 1\\ 1 & 0 & 2 \end{bmatrix}$ $\begin{bmatrix} x1\\ x2\\ x3 \end{bmatrix}$ = $\begin{bmatrix} 0\\ 0\\ \end{bmatrix}$ form (a) a plane. (b) a line. (c) a point. (d) a subspace. (e) the nullspace of A. (f) the column space of A
answered
Apr 27
in
Linear Algebra
by
srestha
Veteran
(
86.9k
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144
views
+1
vote
1
answer
28
EE,2016
Consider a $3\times 3$ matrix with every element being equal to 1 , its only nonzero eigenvalue is ....? $3\times 3 \begin{bmatrix} 1 & 1 &1 \\ 1 &1 &1 \\ 1 &1 &1 \end{bmatrix}$ now i solve in simple way ..directly $\left  A\ ... \\ 0& 0 &0 \\ 0 & 0 &0 \end{bmatrix}$ but i got different eigen values why this happened ... i missed something ??
answered
Apr 25
in
Linear Algebra
by
AsiaPacific
(
43
points)

414
views
0
votes
0
answers
29
ISI 2017 MMA 18
Consider following system of equations: $\begin{bmatrix} 1 &2 &3 &4 \\ 5&6 &7 &8 \\ a&9 &b &10 \\ 6&8 &10 & 13 \end{bmatrix}$$\begin{bmatrix} x1\\ x2\\ x3\\ x4 \end{bmatrix}$=$\begin{bmatrix} 0\\ 0\\ 0\\ 0 \end{bmatrix ... solution for ($x_{1},x_{2},x_{3},x_{4}$) is A) a parabola B) a straight line C) entire $\mathbb{R}^{2}$ D) a point
asked
Apr 25
in
Linear Algebra
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Tesla!
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16.1k
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123
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isi2017
0
votes
1
answer
30
ISI 2017 MMA 16
Let ($x_{n}$) be a sequence of a real number such that the subsequence ($x_{2n}$) and ($x_{3n}$) converge to limit K and L respectively. Then A) ($x_{n}$) always converge B) If K=L then ($x_{n}$) converge C) ($x_{n}$) may not converge but K=L D) it is possible to have K$\neq$L
answered
Apr 25
in
Linear Algebra
by
Kushagra Chatterjee
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8.2k
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104
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isi2017
calculus
engineeringmathematics
0
votes
1
answer
31
ISI 2017 MMA 20
The number of the ordered pair (X, Y), where X and Y are N*N real matrices such that XYYX= I is A) 0 B) 1 C) N D) Infinite
answered
Apr 24
in
Linear Algebra
by
Kushagra Chatterjee
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8.2k
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114
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osi2017
engineeringmathematics
+2
votes
4
answers
32
ISI201729
Suppose the rank of the matrix $$\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$
answered
Apr 24
in
Linear Algebra
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Tesla!
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16.1k
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150
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isi2017
engineeringmathematics
matrices
rankofmatrix
0
votes
1
answer
33
PGEE 2018
let $\left  A \right=8$ ,$\left  B \right=3$ ,$\left  C \right=6$ then what will be value of AB$^{T}$C$^{1}$ A) 144 B) 0 C) 4 D) 14
answered
Apr 22
in
Linear Algebra
by
Akhilesh Singla
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4.7k
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199
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iiithpgee
0
votes
1
answer
34
PGEE 2018
let A and B be two n*n matrices such that they follow commutative property under multiplication operation which of the following follows commutative property 1) $A^{T} B$ 2) $B^{T} A$ 3) $A^{T} B^{T}$ 4) None
answered
Apr 21
in
Linear Algebra
by
Sayan Bose
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2.3k
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99
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iiithpgee
0
votes
2
answers
35
ISRO 2013 Polynomials [EE]
The unique polynomial P(x) of degree 2 such that: P(1) = 1, P(3) = 27, P(4) = 64 is a) 8x2 19x + 12 b) 8x2 + 19x + 12 c) 8x2 19x + 12 d) 8x2 19x  12
answered
Apr 20
in
Linear Algebra
by
sampurnanand mishra
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123
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220
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isro
isroee
engineeringmathematics
0
votes
1
answer
36
Self doubt
There are 10 different balls in such way that 6 balls are white and 4 balls are black. How many different arrangements are possible such way that black ball placed before the white ball ?
answered
Apr 19
in
Linear Algebra
by
Subarna Das
Boss
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10.7k
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46
views
engineeringmathematics
discretemathematics
+1
vote
2
answers
37
linear algebra
answered
Apr 16
in
Linear Algebra
by
pankaj_vir
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8.5k
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51
views
+9
votes
3
answers
38
GATE2004IT6
What values of x, y and z satisfy the following system of linear equations? $$\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 6\\8 \\ 12 \end{bmatrix}$$ $x = 6$, $y = 3$, $z = 2$ $x = 12$, $y = 3$, $z =  4$ $x = 6$, $y = 6$, $z =  4$ $x = 12$, $y =  3$, $z = 0$
answered
Apr 12
in
Linear Algebra
by
Ayush Upadhyaya
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9k
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727
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gate2004it
linearalgebra
systemofequations
easy
+8
votes
2
answers
39
GATE20021.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
answered
Apr 6
in
Linear Algebra
by
Sayed Athar
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93
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567
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gate2002
linearalgebra
easy
matrices
0
votes
1
answer
40
Gate 2004 Question on Linear Algebra
Can Somebody Please explain me in detail description how to calculate the number of upper triangular and lower triangular of a square matrix I read somewhere that it turns out to be ((n^2)+n) /2,Can someone please provide me with a proof
answered
Apr 2
in
Linear Algebra
by
gari
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75
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