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

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

Highest voted questions in Linear Algebra

7 votes
1 answer
125
The equations.$x_{1}+2x_{2}+3x_{3}=1$$x_{1}+4x_{2}+9x_{3}=1$$x_{1}+8x_{2}+27x_{3}=1$haveOnly one solutionTwo solutionsInfinitely many solutionsNo solutions
6 votes
1 answer
128
6 votes
3 answers
129
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 $1$
6 votes
6 answers
131
For the given matrix A, one of the Eigenvalue is real$A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$The ...
6 votes
2 answers
133
The rank of the matrix $A=\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$ is ______ .$0$$1$$2$$3$
5 votes
4 answers
136
Consider the system of equations x+y+z=3x+2y+3z=4x+4y+kz=6 The above system of equations will not have a unique solution for k equals to___
5 votes
5 answers
137
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
5 votes
1 answer
139
5 votes
1 answer
140
If$A=\begin{bmatrix} 1 &2 &2 \\ 2&1 &-2 \\ a&2 &b \end{bmatrix}$then$AAA^{T}=3I$$I$ is a $3\times 3$ identity matrix$\left (a,b \right )$ can be ____________