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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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Most answered questions in Linear Algebra

3 votes
3 answers
101
Made Easy: Linear Algebra (MSQ)
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ has The trivial solution $X=0$. One independent solution. Two independent solution. Three independent solution.
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ hasThe trivial solution $X=0$.One independent solution.Two independent solution.Three independent solution.
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1 votes
3 answers
103
NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are$\text{5 and -5}$$\text{5 and -1}$$\text{1 and -5}$$\text{2 and 3}$
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3 votes
3 answers
104
NIELIT 2016 DEC Scientist B (IT) - Section B: 26
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+​ \sqrt-1)$ and $3$. The determinant of $P$ is ________. $0$ $1$ $15$ $-1$
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+​ \sqrt-1)$ and $3$. The determinant of $P$ is ________.$0$$1$$15$$-1$
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7 votes
3 answers
107
ISI2015-MMA-39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are$1,1,4$$1,4,4$$0,1,4$$0,4,4$
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1 votes
3 answers
109
ISI2015-DCG-22
The value of $\begin{vmatrix} 1 & \log _x y & \log_x z \\ \log _y x & 1 & \log_y z \\ \log _z x & \log _z y & 1 \end{vmatrix}$ is $0$ $1$ $-1$ None of these
The value of $$\begin{vmatrix} 1 & \log _x y & \log_x z \\ \log _y x & 1 & \log_y z \\ \log _z x & \log _z y & 1 \end{vmatrix}$$ is$0$$1$$-1$None of these
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0 votes
3 answers
110
linear algebra
Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are (a) 1024 and−1024 (b) 1024√2 and −1024√2 (c) 4√2 and−4√2 (d) 512√2 and−512√2
Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are(a) 1024 and−1024 (b) 1024√2 and −1024√2(c...
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1 votes
3 answers
112
Matrix
The matrix $A=\begin{bmatrix} 1 &4 \\ 2 &3 \end{bmatrix}$ satisfies the following polynomial $A^{5}-4A^{4}-7A^{3}+11A^{2}-2A+kI=0$ Then the value of k is ______________
The matrix $A=\begin{bmatrix} 1 &4 \\ 2 &3 \end{bmatrix}$satisfies the following polynomial $A^{5}-4A^{4}-7A^{3}+11A^{2}-2A+kI=0$Then the value of k is ______________
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8 votes
3 answers
114
ISI2017-MMA-5
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$? $1$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{2}\right)$
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$?$1$$\left(\dfrac{1}{3}\right)$$\left(\dfrac{1}{6}\right)$$\left(\dfr...
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2 votes
3 answers
115
Mathematics GATE 2018 EE: 44
Let $A$ = $\begin{bmatrix} 1 & 0 & -1 \\-1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B$ = $A^{3} - A^{2} -4A +5I$ where $I$ is the $3\times 3$ identity matrix. The determinant of $B$ is ________ (up to $1$ decimal place).
Let $A$ = $\begin{bmatrix} 1 & 0 & -1 \\-1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B$ = $A^{3} - A^{2} -4A +5I$ where$I$ is the $3\times 3$ identity matrix. The de...
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6 votes
3 answers
116
ISRO-DEC2017-17
If $C$ is a skew-symmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is a scalar matrix null matrix unit matrix matrix will all elements $1$
If $C$ is a skew-symmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is ascalar matrixnull matrixunit matrixmatrix will all elements $1$
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1 votes
3 answers
118
NUMBER of soutions the equations have?
Consider the following system system of equations x1-2x3=0 x1-x2=0 2x1-2x2=0 No solution Infinite number of solutions Three solution unique solution
Consider the following system system of equationsx1-2x3=0x1-x2=02x1-2x2=0 No solution Infinite number of solutions Three solutionunique solution
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