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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 answered questions in Linear Algebra

5 votes
5 answers
32
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
2 votes
5 answers
35
if $A = \begin{bmatrix} 2 &3 &4 \\ 3 & -1 &2 \\ -1& 4 & 5 \end{bmatrix}$ then rank of the matrix $(A-A^T)$ is _____(A) $1$ (B) $2$ (C...
32 votes
5 answers
38
25 votes
5 answers
40
25 votes
5 answers
41
Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$Which of the following is a factor of $\Delta$?$a+b$$a-b...
28 votes
5 answers
43
Obtain the eigen values of the matrix$$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & -2 & 104 \\ 0 & 0 & 0 & -1 \end{bmatrix}$$
79 votes
5 answers
44
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $...
5 votes
4 answers
50
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___