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

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

Recent questions in Linear Algebra

0 votes
0 answers
331
2 votes
2 answers
332
For matrix $p=\begin{bmatrix} 3 &-2 &2 \\ 0 &-2 &1 \\ 0& 0 & 1 \end{bmatrix}$if one of the eigen values is equal to – 2, then which of the following is an eigen vector...
1 votes
2 answers
333
The eigen value of the following matrix in[ 1 1 1 1 1 1 1 1 1 ](a) 1, 1, 1 (b) 1, 0, 0(c) 3, 0, 0 (d) 0, 0, 0
0 votes
0 answers
334
A2 − A = 0, where A is a 9×9 matrix. Then(a) A must be a zero matrix(b) A is an identity matrix(c) rank of A is 1 or 0(d) A is diagonalizable
1 votes
1 answer
338
$\left. \begin{array} { l } { \text { If A is a skew-symmetric matrix of order n, then number of linearly } } \\ { \text { independent eigen vectors of } \left( \mathrm {...
0 votes
1 answer
340
0 votes
1 answer
341
2 votes
1 answer
345
Test the consistency of the following system of equations and solve if possible$3x + 3y +2z = 1$$x + 2y = 4$$10y + 3z = -2$$2x - 3y -z = 5$
2 votes
1 answer
346
Test the consistency of the following system of equations$5x + 3y + 7z = 4 $$3x + 26y + 2z = 9$$7x + 2y + 10z = 5$
5 votes
5 answers
347
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
0 votes
0 answers
349
If $A$ is a $2 \times 2$ matrix such that $trace \: A = det \: A =3$, then what is the trace of $A^{-1}$?$1$$1/3$$1/6$$1/2$
0 votes
0 answers
350