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Recent questions and answers in Linear Algebra
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1
GATE Civil 2021 Set 2 | Question: 2
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is $1$ $2$ $3$ $4$
go_editor
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in
Linear Algebra
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
linear-algebra
matrices
rank-of-matrix
0
votes
0
answers
2
GATE Civil 2021 Set 2 | Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates $AA^{T}=I$ $AA^{T}=0$ $AA^{T}=A^{-1}$ $AA^{T}=A^{2}$
go_editor
asked
in
Linear Algebra
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
linear-algebra
matrices
matrix-algebra
0
votes
0
answers
3
GATE Civil 2021 Set 2 | Question: 27
The smallest eigenvalue and the corresponding eigenvector of the matrix $\begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix}$, respectively, are $1.55$ and $\begin{Bmatrix} 2.00\\ 0.45 \end{Bmatrix}$ $2.00$ ... and $\begin{Bmatrix} -2.55\\ -0.45 \end{Bmatrix}$ $1.55$ and $\begin{Bmatrix} 2.00\\ -0.45 \end{Bmatrix}$
go_editor
asked
in
Linear Algebra
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
4
GATE Civil 2021 Set 1 | Question: 1
The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3\\ 3 & 4 & 2 & 5\\ 5 & 6 & 2 & 7\\ 7 & 8 & 2 & 9 \end{bmatrix}$ is $1$ $2$ $3$ $4$
Arjun
asked
in
Linear Algebra
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
linear-algebra
matrices
rank-of-matrix
0
votes
0
answers
5
GATE Civil 2021 Set 1 | Question: 2
If $P=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $Q=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then $Q^{T}\:P^{T}$ is $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ $\begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}$ $\begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}$ $\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$
Arjun
asked
in
Linear Algebra
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
linear-algebra
matrices
matrix-algebra
0
votes
0
answers
6
GATE2020-CE-1-40
Consider the system of equations $\begin{bmatrix}1&3&2 \\2&2&-3 \\ 4&4&-6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix}$ The value of $x_3$(round off to the nearest integer), is ___________.
go_editor
asked
in
Linear Algebra
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
linear-algebra
matrices
system-of-equations
numerical-answers
0
votes
0
answers
7
GATE2020 CE-2-27
A $4 \times 4$ matrix $[P]$ is given below $[P] = \begin{bmatrix}0 &1 &3 &0 \\-2 &3 &0 &4 \\0 &0 &6 &1 \\0 &0 &1 &6 \end{bmatrix}$ The eigen values of $[P]$ are $0, 3, 6, 6$ $1, 2, 3, 4$ $3, 4, 5, 7$ $1, 2, 5, 7$
go_editor
asked
in
Linear Algebra
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
linear-algebra
matrices
eigen-values
0
votes
0
answers
8
GATE2017 CE-2-1
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants): $3x_1+2x_2=c_1$ $4x_1+x_2=c_2$ The characteristic equation for these simultaneous equation is $\lambda^2 – 4 \lambda – 5=0$ $\lambda^2 – 4 \lambda + 5=0$ $\lambda^2 + 4 \lambda – 5=0$ $\lambda^2 + 4 \lambda + 5=0$
gatecse
asked
in
Linear Algebra
Aug 7, 2019
by
gatecse
4.0k
points
gate2017-ce-2
linear-algebra
system-of-equations
0
votes
0
answers
9
GATE2017 CE-2-28
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to $\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{bmatrix}$ $\begin{bmatrix} 3 & 40 \\ 42 & 8 \end{bmatrix}$ $\begin{bmatrix} 43 & 27 \\ 34 & 50 \end{bmatrix}$ $\begin{bmatrix} 38 & 32 \\ 28 & 56 \end{bmatrix}$
gatecse
asked
in
Linear Algebra
Aug 7, 2019
by
gatecse
4.0k
points
gate2017-ce-2
linear-algebra
matrices
matrix-algebra
0
votes
0
answers
10
GATE2019 CE-2: 1
Euclidean norm (length) of the vector $\begin{bmatrix} 4 & -2 & -6 \end{bmatrix}^T$ is $\sqrt{12}$ $\sqrt{24}$ $\sqrt{48}$ $\sqrt{56}$
Arjun
asked
in
Linear Algebra
Feb 12, 2019
by
Arjun
11.6k
points
gate2019-ce-2
linear-algebra
matrices
unit-vector
1
vote
0
answers
11
GATE2019 CE-2: 35
The inverse of the matrix $\begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}$ is $\begin{bmatrix} 10 & -4 & -9 \\ -15 & 4 & 14 \\ 5 & -1 & -6 \end{bmatrix} \\$ ...
Arjun
asked
in
Linear Algebra
Feb 12, 2019
by
Arjun
11.6k
points
gate2019-ce-2
linear-algebra
matrices
inverse-of-matrix
0
votes
0
answers
12
GATE2016-2-26
Consider the following linear system. $x+2y-3z=a$ $2x+3y+3z=b$ $5x +9y-6z=c$ This system is consistent if $a, b$ and $c$ satisfy the equation $7a-b-c=0$ $3a+b-c=0$ $3a-b+c=0$ $7a-b+c=0$
Milicevic3306
asked
in
Linear Algebra
Mar 28, 2018
by
Milicevic3306
11.9k
points
gate2016-ce-2
linear-algebra
system-of-equations
0
votes
0
answers
13
GATE2016-1-3
If the entries in each column of a square matrix $M$ add up to $1$, then an eigenvalue of $M$ is $4$ $3$ $2$ $1$
Milicevic3306
asked
in
Linear Algebra
Mar 28, 2018
by
Milicevic3306
11.9k
points
gate2016-ce-1
linear-algebra
matrices
eigen-values
0
votes
0
answers
14
GATE2017 CE-1: 1
The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct? $PQ=I$ but $QP \neq I$ $QP=I$ but $PQ \neq I$ $PQ=I$ and $QP= I$ $PQ-QP= I$
Milicevic3306
asked
in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2017-ce-1
linear-algebra
matrices
inverse-of-matrix
0
votes
0
answers
15
GATE2017 CE-1: 28
Consider the matrix $\begin{bmatrix} 5 & -1 \\ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix? Eigenvalue $3$ has a multiplicity of $2$, and only one independent ... has a multiplicity of $2$, and no independent eigenvector exists. Eigenvalues are $3$ and $-3$, and two independent eigenvectors exist.
Milicevic3306
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in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2017-ce-1
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
16
GATE2015-2-5
Let $A=[a_{ij}], \: 1 \leq i, j \leq n$ with $n \geq 3$ and $a_{ij}=i \cdot j$. The rank of $A$ is: $0$ $1$ $n-1$ $n$
Milicevic3306
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in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-2
linear-algebra
matrices
rank-of-matrix
0
votes
0
answers
17
GATE2015-2-28
The two Eigen values of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & p \end{bmatrix}$ have a ratio of $3:1$ for $p=2$. What is another value of $p$ for which the Eigen values have the same ratio of $3:1$? $-2$ $1$ $7/3$ $14/3$
Milicevic3306
asked
in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-2
linear-algebra
matrices
eigen-values
0
votes
0
answers
18
GATE2015-1-1
For what value of $p$ the following set of equations will have no solution? $2x+3y=5$ $3x+py=10$
Milicevic3306
asked
in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-1
numerical-answers
linear-algebra
system-of-equations
0
votes
0
answers
19
GATE2015-1-26
The smallest and largest Eigen values of the following matrix are: $\begin{bmatrix} 3 & -2 & 2 \\ 4 & -4 & 6 \\ 2 & -3 & 5 \end{bmatrix}$ $1.5$ and $2.5$ $0.5$ and $2.5$ $1.0$ and $3.0$ $1.0$ and $2.0$
Milicevic3306
asked
in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-1
linear-algebra
matrices
eigen-values
0
votes
0
answers
20
GATE2014-2-28
The rank of the matrix $\begin{bmatrix} 6 & 0 & 4 & 4 \\ -2 & 14 & 8 & 18 \\ 14 & -14 & 0 & -10 \end{bmatrix}$ is _________
Milicevic3306
asked
in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2014-ce-2
numerical-answers
linear-algebra
matrices
rank-of-matrix
0
votes
0
answers
21
GATE2014-2-2
The determinant of matrix $\begin{bmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 0 \\ 2 & 3 & 0 & 1 \\ 3 & 0 & 1 & 2 \end{bmatrix}$ is ________
Milicevic3306
asked
in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2014-ce-2
numerical-answers
linear-algebra
matrices
determinant
0
votes
0
answers
22
GATE2014-1-4
The sum of Eigen values of the matrix, $[M]$ is where $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$ $915$ $1355$ $1640$ $2180$
Milicevic3306
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in
Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2014-ce-1
linear-algebra
matrices
eigen-values
0
votes
0
answers
23
GATE2014-1-2
Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _______
Milicevic3306
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Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
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gate2014-ce-1
numerical-answers
linear-algebra
matrices
0
votes
0
answers
24
GATE Civil 2013 | Question: 2
What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ columns, and matrix R has $4$ rows and $1$ column. __________
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Linear Algebra
Mar 26, 2018
by
Milicevic3306
11.9k
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gate2013-ce
numerical-answers
linear-algebra
matrices
0
votes
0
answers
25
GATE Civil 2012 | Question: 28
The eigenvalues of matrix $\begin{bmatrix} 9 & 5 \\ 5 & 8 \end{bmatrix}$ are $-2.42$ and $6.86$ $3.48$ and $13.53$ $4.70$ and $6.86$ $6.86$ and $9.50$
Milicevic3306
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in
Linear Algebra
Mar 25, 2018
by
Milicevic3306
11.9k
points
gate2012-ce
linear-algebra
matrices
eigen-values
0
votes
1
answer
26
GATE2018 CE-1: 1
Which one of the following matrices is singular? $\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 2 & 4\\ 3 & 6 \end{bmatrix} \\$ $\begin{bmatrix} 4 & 3\\ 6 & 2 \end{bmatrix}$
goudarningu
answered
in
Linear Algebra
Feb 24, 2018
by
goudarningu
360
points
gate2018-ce-1
linear-algebra
matrices
determinant
0
votes
1
answer
27
GATE2018 CE-2: 26
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ has real eigenvalues and eigenvectors real eigenvalues but complex eigenvectors complex eigenvalues but real eigenvectors complex eigenvalues and eigenvectors
paiyyawulpuja
answered
in
Linear Algebra
Feb 20, 2018
by
paiyyawulpuja
120
points
gate2018-ce-2
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
28
GATE2018 CE-2: 28
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$ $1$ $2$ $3$ $4$
gatecse
asked
in
Linear Algebra
Feb 17, 2018
by
gatecse
4.0k
points
gate2018-ce-2
linear-algebra
matrices
rank-of-matrix
0
votes
0
answers
29
GATE2018 CE-1: 2
For the given orthogonal matrix Q, $Q = \begin{bmatrix} 3/7 & 2/7 & 6/7 \\ -6/7 & 3/7 & 2/7 \\ 2/7 & 6/7 & -3/7 \end{bmatrix}$ ... $\begin{bmatrix} -3/7 & 6/7 & -2/7 \\ -2/7 & -3/7 & -6/7 \\ -6/7 & -2/7 & 3/7 \end{bmatrix}$
gatecse
asked
in
Linear Algebra
Feb 17, 2018
by
gatecse
4.0k
points
gate2018-ce-1
linear-algebra
matrices
orthogonal-matrix
inverse-of-matrix
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Recent questions and answers in Linear Algebra