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Recent questions and answers in Linear Algebra
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GATE IN 2021 | Question: 1
Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is $1$ $2$ $3$ $4$
Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is$1$$2$$3$$4$
Arjun
2.9k
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Arjun
asked
Feb 19, 2021
Linear Algebra
gatein-2021
linear-algebra
matrices
rank-of-matrix
vectors
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0
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0
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2
GATE IN 2021 | Question: 25
The determinant of the matrix $\text{M}$ shown below is _______________. $M=\begin{bmatrix} 1 & 2 & 0 & 0\\ 3 & 4 & 0 & 0\\ 0 & 0 & 4 & 3\\ 0 & 0 & 2 & 1 \end{bmatrix}$
The determinant of the matrix $\text{M}$ shown below is _______________. $$M=\begin{bmatrix} 1 & 2 & 0 & 0\\ 3 & 4 & 0 & 0\\ 0 & 0 & 4 & 3\\ 0 & 0 & 2 & 1 \end{bmatrix}$$...
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Linear Algebra
gatein-2021
numerical-answers
linear-algebra
matrices
determinant
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–
0
votes
0
answers
3
GATE IN 2021 | Question: 38
Given $A=\begin{pmatrix} 2 & 5\\ 0 & 3 \end{pmatrix}$. The value of the determinant $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
Given $A=\begin{pmatrix} 2 & 5\\ 0 & 3 \end{pmatrix}$. The value of the determinant $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Linear Algebra
gatein-2021
numerical-answers
linear-algebra
matrices
determinant
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–
0
votes
0
answers
4
GATE2020 IN: 26
Consider the matrix $M=\begin {bmatrix} 1&-1&0\\1&-2&1\\0&-1&1\end{bmatrix}$. One of the eigenvectors of $M$ is $\begin {bmatrix} 1\\-1\\1\end{bmatrix}$ $\begin {bmatrix} 1\\1\\-1\end{bmatrix}$ $\begin {bmatrix} -1\\1\\-1\end{bmatrix}$ $\begin {bmatrix} 1\\1\\1\end{bmatrix}$
Consider the matrix $M=\begin {bmatrix} 1&-1&0\\1&-2&1\\0&-1&1\end{bmatrix}$. One of the eigenvectors of $M$ is$\begin {bmatrix} 1\\-1\\1\end{bmatrix}$$\begin {bmatrix} 1...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Linear Algebra
gate2020-in
linear-algebra
matrices
eigen-values
eigen-vectors
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–
0
votes
0
answers
5
GATE2020: 3
A set of linear equations is given in the form $Ax=b$, where A is a $2\times 4$ matrix with real number entries and $b\neq 0.$ will it be possible to solve for $x$ and obtain a unique solution by multiplying both left and right sides of the equation by $A^T$ (the super script $T$ denotes the transpose) and ... $A^T A$ is well conditioned Yes, can obtain a unique solution provided the matrix $A$ is well conditioned
A set of linear equations is given in the form $Ax=b$, where A is a $2\times 4$ matrix with real number entries and $b\neq 0.$ will it be possible to solve for $x$ and ob...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Linear Algebra
gate2020-in
linear-algebra
matrices
matrix-algebra
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–
0
votes
0
answers
6
GATE2017: 1
If $\text{v}$ is a non-zero vector of dimensions $3\times1$, then the matrix $A=VV^T$ has a rank = ____________.
If $\text{v}$ is a non-zero vector of dimensions $3\times1$, then the matrix $A=VV^T$ has a rank = ____________.
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 1, 2020
Linear Algebra
gate2017-in
numerical-answers
linear-algebra
matrices
rank-of-matrix
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–
0
votes
0
answers
7
GATE2017: 2
The figure shows a shape $\text ABC$ and its mirror image $\text A_1B_1C_1$ across the horizontal axis $\text (X-axis)$. The coordinate transformation matrix that maps $\text ABC$ to $\text A_1B_1C_1$ is $\begin{bmatrix}0&1\\1 &0\end{bmatrix}$ $\begin{bmatrix}0 &1\\-1 &0\end{bmatrix}$ $\begin{bmatrix}-1 &0\\0 &1\end{bmatrix}$ $\begin{bmatrix}1 &0\\0 &-1\end{bmatrix}$
The figure shows a shape $\text ABC$ and its mirror image $\text A_1B_1C_1$ across the horizontal axis $\text (X-axis)$. The coordinate transformation matrix that maps $\...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 1, 2020
Linear Algebra
gate2017-in
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
8
GATE2017: 4
The eigenvalues of the matrix $A=\begin{bmatrix}1 &-1 &5\\0 &5 &6\\0 &-6 &5\end{bmatrix}$ are $-1,\;5,\;6$ $1,\;-5\pm j6$ $1,\;5\pm j6$ $1,\;5,\;5$
The eigenvalues of the matrix $A=\begin{bmatrix}1 &-1 &5\\0 &5 &6\\0 &-6 &5\end{bmatrix}$ are$-1,\;5,\;6$$1,\;-5\pm j6$$1,\;5\pm j6$$1,\;5,\;5$
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 1, 2020
Linear Algebra
gate2017-in
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
9
GATE2019 IN: 16
A 3 x 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is $\_\_\_\_$.
A 3 x 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is $\_\_\_\_$.
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Linear Algebra
gate2019-in
numerical-answers
linear-algebra
matrices
eigen-values
determinant
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–
0
votes
0
answers
10
GATE2016-28
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_\_.$
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2016-in
numerical-answers
linear-algebra
matrices
eigen-values
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–
0
votes
0
answers
11
GATE2015-11
Let $A$ be an $n\times n$ matrix with rank $r(0<r<n).$ Then $\text{Ax=0}$ has $p$ independent solutions, where $p$ is $r$ $n$ $n-r$ $n+r$
Let $A$ be an $n\times n$ matrix with rank $r(0<r<n).$ Then $\text{Ax=0}$ has $p$ independent solutions, where $p$ is$r$$n$$n-r$$n+r$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2015-in
linear-algebra
matrices
system-of-equations
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–
0
votes
0
answers
12
GATE2014-26
A scalar valued function is defined as $f(X)=X^TAX+b^TX+c,$ where A is a symmetric positive definite matrix with dimension $n\times n$; b and X are vectors of dimension $n\times 1$. The minimum value of f(x) will occur when X equals $(A^TA)^{-1}b$ $-(A^TA)^{-1}b$ $-(\frac{A^{-1}b}{2})$ $\frac{A^{-1}b}{2}$
A scalar valued function is defined as $f(X)=X^TAX+b^TX+c,$ where A is a symmetric positive definite matrix with dimension $n\times n$; b and X are vectors of dimension $...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-in
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
13
GATE2014-28
For the matrix $A$ satisfying the equation given below, the eigenvalues are $[A] \begin {bmatrix} 1&2&3\\7&8&9\\4&5&6\end{bmatrix}=\begin {bmatrix} 1&2&3\\4&5&6\\7&8&9\end{bmatrix}$ $(1,-j,j)$ $(1,1,0)$ $(1,1,-1)$ $(1,0,0)$
For the matrix $A$ satisfying the equation given below, the eigenvalues are$$[A] \begin {bmatrix} 1&2&3\\7&8&9\\4&5&6\end{bmatrix}=\begin {bmatrix} 1&2&3\\4&5&6\\7&8&9\en...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-in
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
14
GATE2013-27
One pair of eigenvectors corresponding to the two eigenvalues of the matrix $\begin{bmatrix}0&-1\\1&0\end{bmatrix}$ is $\begin{bmatrix}1\\-j\end{bmatrix}$,$\begin{bmatrix}j\\-1\end{bmatrix}$ $\begin{bmatrix}0\\1\end{bmatrix}$,$\begin{bmatrix}-1\\0\end{bmatrix}$ $\begin{bmatrix}1\\j\end{bmatrix}$,$\begin{bmatrix}0\\1\end{bmatrix}$ $\begin{bmatrix}1\\j\end{bmatrix}$,$\begin{bmatrix}j\\1\end{bmatrix}$
One pair of eigenvectors corresponding to the two eigenvalues of the matrix $\begin{bmatrix}0&-1\\1&0\end{bmatrix}$ is$\begin{bmatrix}1\\-j\end{bmatrix}$,$\begin{bmatrix}...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-in
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
0
answers
15
GATE2013-1
The dimension of the null space of the matrix $\begin{bmatrix} 0&1&1\\1&-1&0\\-1&0&-1 \end{bmatrix}$ is $0$ $1$ $2$ $3$
The dimension of the null space of the matrix $\begin{bmatrix} 0&1&1\\1&-1&0\\-1&0&-1 \end{bmatrix}$ is$0$$1$$2$$3$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-in
linear-algebra
matrices
null-space
+
–
0
votes
0
answers
16
GATE2012-27
Given that $A=\begin{bmatrix}-5 &-3\\2 &0\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 &1\end{bmatrix}$, the value of $A^3$ is $15A+12I$ $19A+30I$ $17A+15I$ $17A+21I$
Given that$A=\begin{bmatrix}-5 &-3\\2 &0\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 &1\end{bmatrix}$, the value of $A^3$ is$15A+12I$$19A+30I$$17A+15I$$17A+21I$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012-in
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
17
GATE2018IN: 28
Consider the following system of linear equations: 3x + 2ky = -2 kx + 6y =2 Here x and y are the unknows and k is real constant. The value of k for which there are infinite number of solutions is 3 1 -3 -6
Consider the following system of linear equations: 3x + 2ky = -2 kx + 6y =2Here x and y are the unknows and k is real c...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Linear Algebra
gate2018-in
linear-algebra
system-of-equations
+
–
0
votes
0
answers
18
GATE2018IN: 1
Let N be a 3 by 3 matrix with real numbers entries. The matrix N is such that N$^2$ = 0. The eigen values of N are 0, 0, 0 0,0,1 0,1,1 1,1,1
Let N be a 3 by 3 matrix with real numbers entries. The matrix N is such that N$^2$ = 0. The eigen values of N are 0, 0, 00,0,10,1,11,1,1
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Linear Algebra
gate2018-in
linear-algebra
matrices
eigen-values
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