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Syllabus: Matrices, determinants, System of linear equations, Eigenvalues and eigenvectors, LU decomposition.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &0&1&0&1&1&1&1&1&2&0&0.9&2
\\\hline\textbf{2 Marks Count} & 2 &1&1&1&1&1&2&1&0&0&0&1&2
\\\hline\textbf{Total Marks} & 5 &2&3&2&3&3&5&3&1&2&\bf{1}&\bf{2.9}&\bf{5}\\\hline
\end{array}}}$$

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Recent questions in Linear Algebra

1 votes
1 answer
241
GATE Overflow Test Series | Mixed Subjects | Test 4 | Question: 5
Given an orthogonal matrix $A,$ $(AA^{T})^{-1}$ is _______ $2I$ $I$ $I/2$ $A$
Given an orthogonal matrix $A,$ $(AA^{T})^{-1}$ is _______$2I$$I$$I/2$$A$
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1 votes
1 answer
242
GATE Overflow Test Series | Mixed Subjects | Test 4 | Question: 6
If $A = \begin{bmatrix}-12 & 7\\ -5 & 3 \end{bmatrix},$ then the value of $\text{det}(A^{2021})$ is _________
If $A = \begin{bmatrix}-12 & 7\\ -5 & 3 \end{bmatrix},$ then the value of $\text{det}(A^{2021})$ is _________
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1 votes
1 answer
243
GATE Overflow Test Series | Mixed Subjects | Test 4 | Question: 7
If det $\begin{pmatrix} 2 &\alpha\\ 3 & \beta \end{pmatrix} = 16$ and det $\begin{pmatrix} 2 &\beta\\ 3 & \alpha \end{pmatrix} = 1,$ then the value of $\alpha^{2} + \beta^{2}$ is _________
If det $\begin{pmatrix}2 &\alpha\\3 & \beta\end{pmatrix} = 16$ and det $\begin{pmatrix}2 &\beta\\3 & \alpha\end{pmatrix} = 1,$ then the value of $\alpha^{2} + \beta^{2}$ ...
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1 votes
1 answer
246
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 1
Let $P = [p_{ij}],$ where $1 \leq i,j \leq n$ is defined by $p_{ij} = i\times j, \forall i,j$ with $n > 2.$ The rank of $P$ is _______
Let $P = [p_{ij}],$ where $1 \leq i,j \leq n$ is defined by $p_{ij} = i\times j, \forall i,j$ with $n 2.$ The rank of $P$ is _______
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3 votes
1 answer
248
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 3
The value of the determinant $\begin{vmatrix} 2\alpha & \alpha + \beta & \alpha + \gamma\\ \beta + \alpha & 2\beta & \beta + \gamma\\ \gamma + \alpha & \gamma + \beta & 2\gamma \end{vmatrix}$ is ________
The value of the determinant $\begin{vmatrix}2\alpha & \alpha + \beta & \alpha + \gamma\\\beta + \alpha & 2\beta & \beta + \gamma\\\gamma + \alpha & \gamma + \beta & 2\ga...
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3 votes
2 answers
249
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 4
Given a matrix $A = \dfrac{1}{2} \begin{bmatrix} 1 &1 &1 &1 \\ 1 &-1 &1 &-1 \\ 1 &1 &-1 &-1 \\ 1& -1 &-1 &1 \end{bmatrix},$ then $(AA^{-1})^{T}$ is _______ $I$ $\frac{1}{2} I$ $4I$ $\frac{1}{4}I$
Given a matrix $A = \dfrac{1}{2} \begin{bmatrix} 1 &1 &1 &1 \\ 1 &-1 &1 &-1 \\ 1 &1 &-1 &-1 \\ 1& -1 &-1 &1 \end{bmatrix},$ then $(AA^{-1})^{T}$ is _______$I$$\frac{1}{2}...
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2 votes
1 answer
250
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 5
If $A =\begin{bmatrix} 1 & 0 & 0\\ 0 & 0 & 1\\ 0 & 1 & 0 \end{bmatrix},$ the value of $(A^{-1})^{T}$ is _____ (Mark all the appropriate choices) $A$ $Adj\;A$ $\left(\left(A^{T}\right)^{T}\right)^{T}$ $A^{T}$
If $A =\begin{bmatrix}1 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix},$ the value of $(A^{-1})^{T}$ is _____(Mark all the appropriate choices)$A$$Adj\;A$$\left(\left(A^{T}\r...
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1 votes
1 answer
252
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 7
If $A$ is an $n \times n$ non-singular matrix, such that $AA^{T} = A^{T}A$ and $B = A^{-1}A^{T},$ then $BB^{T}$ is equal to _____ (Mark all the appropriate choices) $I$ $B^{-1}$ $(B^{-1})^{T}$ $I^{T}$
If $A$ is an $n \times n$ non-singular matrix, such that $AA^{T} = A^{T}A$ and $B = A^{-1}A^{T},$ then $BB^{T}$ is equal to _____ (Mark all the appropriate choices)$I$$B^...
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5 votes
1 answer
253
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 8
If $A$ is skew- symmetric matrix of order $3,$ then the matrix $A^{6}$ is? Diagonal matrix Skew-symmetric matrix Symmetric matrix None of the above
If $A$ is skew- symmetric matrix of order $3,$ then the matrix $A^{6}$ is?Diagonal matrixSkew-symmetric matrixSymmetric matrixNone of the above
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1 votes
1 answer
256
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 11
If $A = \begin{bmatrix} 1&-3 & -4\\ -1 & 3 & 4\\ 1 & -3 & -4 \end{bmatrix},$ is a nilpotent matrix, its index is _______
If $A = \begin{bmatrix}1&-3 & -4\\-1 & 3 & 4\\1 & -3 & -4\end{bmatrix},$ is a nilpotent matrix, its index is _______
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1 votes
1 answer
258
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 13
The determinant of the matrix ... is _________
The determinant of the matrix $A = \begin{pmatrix}\frac{1}{2}& \alpha & 1 & 1 & 1 & 1 & 1 & 1\\0 & -2 & 1 & 1 & 2 & -3 & 8 & -9\\0 & 0 & -88 & 0 & 0 & 0 & 2 & 0\\0 & 0 & ...
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1 votes
1 answer
259
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 14
The value of $\begin{vmatrix} a^{2} & a & bc\\ b^{2} & b & ca\\ c^{2} & c & ab \end{vmatrix} + \begin{vmatrix} 1 & 1 & 1\\ a^{2} & b^{2} & c^{2}\\ a^{3} & b^{3} & c^{3} \end{vmatrix} =$ ________
The value of $\begin{vmatrix}a^{2} & a & bc\\b^{2} & b & ca\\c^{2} & c & ab\end{vmatrix} + \begin{vmatrix}1 & 1 & 1\\a^{2} & b^{2} & c^{2}\\a^{3} & b^{3} & c^{3}\end{vmat...
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