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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

1 votes
4 answers
61
$\begin{pmatrix}4&3 \\6&3 \end{pmatrix}$What is the sum of all the elements of the $L$ and $U$ matrices as obtained in the L U decomposition?$16$$10$$9$$6$
18 votes
4 answers
66
The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is:$0$$1$$2$$3$
60 votes
4 answers
67
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________
20 votes
4 answers
68
The rank of the matrix given below is:$$\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$$$3$$1$$2$$4$
22 votes
4 answers
71
Consider the following matrix $$A = \left[\begin{array}{cc}2 & 3\\x & y \end{array}\right]$$ If the eigenvalues of A are $4$ and $8$, then$x = 4$, $y = 10$$x = 5$, $y = 8...
35 votes
4 answers
72
28 votes
4 answers
73
How many solutions does the following system of linear equations have?$-x + 5y = -1$$x - y = 2$$x + 3y = 3$infinitely manytwo distinct solutionsuniquenone
35 votes
4 answers
74
Let $A, B, C, D$ be $n \times n$ matrices, each with non-zero determinant. If $ABCD = I$, then $B^{-1}$ is $D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily e...
33 votes
4 answers
75
Consider the following system of linear equations $$\left( \begin{array}{ccc} 2 & 1 & -4 \\ 4 & 3 & -12 \\ 1 & 2 & -8 \end{array} \right) \left( \begin{array}{ccc} x \\ y...
0 votes
3 answers
76
0 votes
3 answers
77
It is given that m < nlets consider m = 4 and n = 5.If rank(A) = n, this means no of linearly independent columns in A are 5, but we cannot have 5 linearly independent ve...
3 votes
3 answers
79
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.