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

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

Most viewed questions in Linear Algebra

10 votes
2 answers
121
If $\text{A}$ and $\text{B}$ are square matrices with same order and $\text{A}$ is symmetric, then $\text{B}^{\text{T}}\text{AB}$ isSkew symmetricSymmetricOrthogonalIdemp...
2 votes
3 answers
122
0 votes
2 answers
123
1 votes
1 answer
124
10 votes
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126
$\begin{vmatrix} 265 && 240 && 219 \\ 240 && 225 && 198 \\ 219 && 198 && 181 \\ \end{vmatrix} = $$779$$679$$0$$256$
1 votes
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127
If the entries in each column of a square matrix M add up to 1, then an eigen value of M isA) 4 B) 3 C) 2 D) 1
8 votes
4 answers
128
If a square matrix A satisfies $A^TA=I$, then the matrix $A$ isIdempotentSymmetricOrthogonalHermitian
4 votes
2 answers
131
Nullity of a matrix = Total number columns – Rank of that matrixBut how to calculate value of x when nullity is already given(1 in this case)
8 votes
3 answers
132
5 votes
1 answer
133
1 votes
1 answer
134
3 votes
2 answers
135
Let $A$ be a $3\times 4$ matrix.The system of equations $Ax=0$ hasunique solutionInfinite solutionNo solutionExactly 2 solutions
0 votes
2 answers
137
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=?a)24b)-2c)12d)-12Please explain in detail.
3 votes
1 answer
138