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Recent questions and answers in Linear Algebra
1
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votes
GATE Mechanical 2021 Set 2 | Question: 1
Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $p.$ Their product $Ap=\alpha ^{2}p$, where $\alpha \in \Re$ and $\alpha \notin \left \{ -1,0,1 \right \}$. Based on the given information, the eigen value of $A^{2}$ is: $\alpha$ $\alpha ^{2}$ $\surd{\alpha }$ $\alpha ^{4}$
ShouvikSVK
answered
in
Linear Algebra
Jan 22, 2022
by
ShouvikSVK
280
points
gateme-2021-set2
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 27
Let the superscript $\text{T}$ represent the transpose operation. Consider the function $f(x)=\frac{1}{2}x^TQx-r^Tx$, where $x$ and $r$ are $n \times 1$ vectors and $\text{Q}$ is a symmetric $n \times n$ matrix. The stationary point of $f(x)$ is $Q^{T}r$ $Q^{-1}r$ $\frac{r}{r^{T}r}$ $r$
go_editor
asked
in
Linear Algebra
Mar 1, 2021
by
go_editor
5.0k
points
gateme-2021-set2
linear-algebra
matrix-algebra
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 26
Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an eigenvector of a $2\times2$ matrix $\text{A}$ ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
gatecse
asked
in
Linear Algebra
Feb 22, 2021
by
gatecse
1.6k
points
gateme-2021-set1
linear-algebra
eigen-values
eigen-vectors
1
answer
0
votes
GATE2020-ME-2: 2
A matrix $P$ is decomposed into its symmetric part $S$ and skew symmetric part $V$ ... $\begin{pmatrix} -2 & 9/2 & -1 \\ -1 & 81/4 & 11 \\ -2 & 45/2 & 73/4 \end{pmatrix}$
haralk10
answered
in
Linear Algebra
Dec 2, 2020
by
haralk10
180
points
gateme-2020-set2
linear-algebra
matrices
0
answers
0
votes
GATE2020-ME-2: 19
Let $\textbf{I}$ be a $100$ dimensional identity matrix and $\textbf{E}$ be the set of its distinct (no value appears more than once in $\textbf{E})$ real eigen values. The number of elements in $\textbf{E}$ is _________
go_editor
asked
in
Linear Algebra
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
numerical-answers
linear-algebra
eigen-values
0
answers
0
votes
GATE2020-ME-1: 1
Multiplication of real valued square matrices of same dimension is associative commutative always positive definite not always possible to compute
go_editor
asked
in
Linear Algebra
Feb 19, 2020
by
go_editor
5.0k
points
gateme-2020-set1
linear-algebra
matrices
1
answer
0
votes
GATE2017 ME-2: 28
Consider the matrix $A=\begin{bmatrix} 50 &70 \\ 70 & 80 \end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda _{1}$ and $\lambda _{2}$ are $x_{1}=\begin{bmatrix} 70 \\ \lambda_{1}-50 \end{bmatrix}$ and $x_{2}=\begin{bmatrix} \lambda _{2}-80\\ 70 \end{bmatrix}$, respectively. The value of $x^{T}_{1} x_{2}$ is _________.
ankitgupta.1729
answered
in
Linear Algebra
May 24, 2019
by
ankitgupta.1729
410
points
gateme-2017-set2
numerical-answers
linear-algebra
eigen-values
eigen-vectors
1
answer
0
votes
GATE2019 ME-2: 1
In matrix equation $[A] \{X\}=\{R\}$, $[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{ and} \{ R \} = \begin{Bmatrix} 32 \\ 16 \\ 64 \end{Bmatrix}$ One of the eigen values of matrix $[A]$ is $4$ $8$ $15$ $16$
ankitgupta.1729
answered
in
Linear Algebra
May 24, 2019
by
ankitgupta.1729
410
points
gateme-2019-set2
linear-algebra
matrices
eigen-values
1
answer
1
vote
GATE2019 ME-1: 1
Consider the matrix $P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ The number of distinct eigenvalues $0$ $1$ $2$ $3$
aditya_kr
answered
in
Linear Algebra
Feb 15, 2019
by
aditya_kr
160
points
gateme-2019-set1
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2019 ME-2: 18
The transformation matrix for mirroring a point in $x – y$ plane about the line $y=x$ is given by $\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \\$ $\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix} \\$ $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \\$ $\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}$
Arjun
asked
in
Linear Algebra
Feb 9, 2019
by
Arjun
27.5k
points
gateme-2019-set2
linear-algebra
matrix-algebra
0
answers
0
votes
GATE2019 ME-1: 26
The set of equations $\begin{array}{l} x+y+z=1 \\ ax-ay+3z=5 \\ 5x-3y+az=6 \end{array}$ has infinite solutions, if $a=$ $-3$ $3$ $4$ $-4$
Arjun
asked
in
Linear Algebra
Feb 9, 2019
by
Arjun
27.5k
points
gateme-2019-set1
linear-algebra
system-of-equations
0
answers
0
votes
GATE ME 2012 | Question: 47
$x+2y+z=4$ $2x+y+2z=5$ $x-y+z=1$ The system of algebraic equations given above has a unique solution of $x=1$, $y=1$ and $z=1$ only the two solutions of $(x=1, y=1, z=1)$ and $(x=2, y=1, z=0)$ infinite number of solutions no feasible solution
Andrijana3306
asked
in
Linear Algebra
Mar 20, 2018
by
Andrijana3306
1.5k
points
gateme-2012
linear-algebra
system-of-equations
0
answers
0
votes
GATE ME 2012 | Question: 36
For the matrix $A = \begin{bmatrix} 5 & 3 \\ 1 & 3 \end{bmatrix}$, ONE of the normalized eigen vectors is given as $\begin{pmatrix} \dfrac{1}{2} \\ \dfrac{\sqrt{3}}{2} \end{pmatrix} \\$ ... $\begin{pmatrix} \dfrac{1}{\sqrt{5}} \\ \dfrac{2}{\sqrt{5}} \end{pmatrix}$
Andrijana3306
asked
in
Linear Algebra
Mar 20, 2018
by
Andrijana3306
1.5k
points
gateme-2012
linear-algebra
eigen-values
eigen-vectors
1
answer
0
votes
GATE2018-2-19
If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{-1})$ is _______ (correct to two decimal palces).
Balaji Jegan
answered
in
Linear Algebra
Feb 22, 2018
by
Balaji Jegan
1.2k
points
gateme-2018-set2
numerical-answers
linear-algebra
matrices
rank-of-matrix
0
answers
0
votes
GATE2018-1-2
The rank of the matrix $\begin{bmatrix} -4 & 1 & -1 \\ -1 & -1 & -1 \\ 7 & -3 & 1 \end{bmatrix}$ is $1$ $2$ $3$ $4$
Arjun
asked
in
Linear Algebra
Feb 17, 2018
by
Arjun
27.5k
points
gateme-2018-set1
linear-algebra
matrices
rank-of-matrix
1
answer
0
votes
GATE2017 ME-2: 3
The determinant of a $2 \times 2$ matrix is $50$. If one eigenvalue of the matrix is $10$, the other eigenvalue is _________.
m2n037
answered
in
Linear Algebra
Feb 14, 2018
by
m2n037
940
points
gateme-2017-set2
numerical-answers
linear-algebra
matrices
eigen-values
1
answer
0
votes
GATE Mechanical 2014 Set 4 | Question: 1
Which one of the following equations is a correct identity for arbitrary $3 \times 3$ real matrices $P$, $Q$ and $R$? $P(Q+R)=PQ+RP$ $(P-Q)^2 = P^2 -2PQ -Q^2$ $\text{det } (P+Q)= \text{det } P+ \text{det } Q$ $(P+Q)^2=P^2+PQ+QP+Q^2$
annie1234
answered
in
Linear Algebra
Apr 6, 2017
by
annie1234
460
points
gateme-2014-set4
linear-algebra
matrices
matrix-algebra
0
answers
0
votes
GATE2017 ME-1: 26
Consider the matrix $P=\begin{bmatrix} \dfrac{1}{\sqrt{2}} & 0 &\dfrac{1}{\sqrt{2}} \\ 0 & 1 & 0\\ -\dfrac{1}{\sqrt{2}} &0 & \dfrac{1}{\sqrt{2}} \end{bmatrix}$ Which one of the following statements about $P$ is INCORRECT ? Determinant of P is equal to $1$. $P$ is orthogonal. Inverse of $P$ is equal to its transpose. All eigenvalues of $P$ are real numbers.
Arjun
asked
in
Linear Algebra
Feb 27, 2017
by
Arjun
27.5k
points
gateme-2017-set1
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2017 ME-1: 1
The product of eigenvalues of the matrix $P$ is $P=\begin{bmatrix} 2 & 0 & 1\\ 4& -3 &3 \\ 0 & 2 & -1 \end{bmatrix}$ $-6$ $2$ $6$ $-2$
Arjun
asked
in
Linear Algebra
Feb 27, 2017
by
Arjun
27.5k
points
gateme-2017-set1
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2016-3-26
The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.5k
points
gateme-2016-set3
numerical-answers
linear-algebra
eigen-values
eigen-vectors
0
answers
0
votes
GATE2016-3-1
A real square matrix $\textbf{A}$ is called skew-symmetric if $A^T=A$ $A^T=A^{-1}$ $A^T=-A$ $A^T=A+A^{-1}$
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.5k
points
gateme-2016-set3
linear-algebra
matrices
0
answers
0
votes
GATE2016-2-1
The condition for which the eigenvalues of the matrix $A=\begin{bmatrix} 2 & 1\\ 1 & k \end{bmatrix}$ are positive, is $k > 1/2$ $k > −2$ $k > 0$ $k < −1/2$
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.5k
points
gateme-2016-set2
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2016-1-1
The solution to the system of equations $\begin{bmatrix} 2 & 5\\-4 &3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\ -30 \end{bmatrix}$ is $6,2$ $-6,2$ $-6,-2$ $6,-2$
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.5k
points
gateme-2016-set1
linear-algebra
matrices
system-of-equations
0
answers
0
votes
GATE2015-3-42
For a given matrix $P=\begin{bmatrix} 4+3i & -i\\ i & 4-3i \end{bmatrix}$, where $i=\sqrt{-1}$, the inverse of matrix $P$ is $P=\displaystyle{\frac{1}{24}}\begin{bmatrix} 4-3i & i\\ -i & 4+3i \end{bmatrix} \\$ ... $P=\displaystyle{\frac{1}{25}}\begin{bmatrix} 4+3i & -i\\ i & 4-3i \end{bmatrix} \\$
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.5k
points
gateme-2015-set3
linear-algebra
matrices
0
answers
0
votes
GATE2015-3-15
The lowest eigenvalue of the $2\times 2$ matrix $\begin{bmatrix} 4 & 2\\ 1 & 3 \end{bmatrix}$ is ________
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.5k
points
gateme-2015-set3
numerical-answers
linear-algebra
matrices
eigenvalues
0
answers
0
votes
GATE2015-2-1
At least one eigenvalue of a singular matrix is positive zero negative imaginary
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.5k
points
gateme-2015-set2
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2015-1-1
If any two columns of a determinant $P=\begin{bmatrix} 4 & 7 & 8\\ 3 & 1 & 5\\ 9 & 6 & 2 \end{bmatrix}$ are interchanged, which one of the following statements regarding the value of the determinant is CORRECT? ... . Both absolute value and sign will change. Absolute value will change but sign will not change. Both absolute value and sign will remain unchanged.
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.5k
points
gateme-2015-set1
linear-algebra
matrices
0
answers
0
votes
GATE Mechanical 2014 Set 3 | Question: 1
Consider a $3×3$ real symmetric matrix S such that two of its eigenvalues are $a\neq 0$, $b\neq 0$ with respective eigenvectors $\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$, $\begin{bmatrix} y_1\\ y_2\\ y_3 \end{bmatrix}$ If $a\neq b$ then $x_1y_1+x_2y_2+x_3y_3$ equals $a$ $b$ $ab$ $0$
Arjun
asked
in
Linear Algebra
Feb 19, 2017
by
Arjun
27.5k
points
gateme-2014-set3
linear-algebra
matrices
eigen-values
eigen-vectors
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 18
If there are $m$ sources and $n$ destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is $m + n$ $m + n + 1$ $m + n − 1$ $m$
Arjun
asked
in
Linear Algebra
Feb 19, 2017
by
Arjun
27.5k
points
gateme-2014-set2
linear-algebra
matrix-algebra
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 1
One of the eigen vectors of the matrix $\begin{bmatrix} -5 & 2\\ -9 & 6 \end{bmatrix}$ is $\begin{Bmatrix} -1\\ 1 \end{Bmatrix} \\$ $\begin{Bmatrix} -2\\ 9 \end{Bmatrix} \\$ $\begin{Bmatrix} 2\\ -1 \end{Bmatrix} \\$ $\begin{Bmatrix} 1\\ 1 \end{Bmatrix} \\$
Arjun
asked
in
Linear Algebra
Feb 19, 2017
by
Arjun
27.5k
points
gateme-2014-set2
linear-algebra
eigen-values
eigen-vectors
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 4
The matrix form of the linear syatem $\dfrac{dx}{dt}=3x-5y$ and $\dfrac{dy}{dt}=4x+8y$ is $\dfrac{d}{dt}\begin{Bmatrix} x\\y \end{Bmatrix}=\begin{bmatrix} 3 & -5\\ 4& 8 \end{bmatrix}\begin{Bmatrix} x\\y \end{Bmatrix} \\$ ...
Arjun
asked
in
Linear Algebra
Feb 19, 2017
by
Arjun
27.5k
points
gateme-2014-set1
linear-algebra
matrices
matrix-algebra
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 1
Given that the determinant of the matrix $\begin{bmatrix} 1 & 3 & 0\\ 2 & 6 & 4\\ -1 & 0 & 2 \end{bmatrix}$ is $-12$, the determinant of the matrix $\begin{bmatrix} 2 & 6 & 0\\ 4 & 12 & 18\\ -2 & 0 & 4 \end{bmatrix}$ is $-96$ $-24$ $24$ $96$
Arjun
asked
in
Linear Algebra
Feb 19, 2017
by
Arjun
27.5k
points
gateme-2014-set1
linear-algebra
matrices
determinant
0
answers
0
votes
GATE ME 2013 | Question: 2
The eigen values of a symmetric matrix are all complex with non-zero positive imaginary part. complex with non-zero negative imaginary part. real. pure imaginary.
piyag476
asked
in
Linear Algebra
Feb 19, 2017
by
piyag476
1.4k
points
gateme-2013
linear-algebra
matrices
eigen-values
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Recent questions and answers in Linear Algebra