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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

1 votes
4 answers
272
$\begin{pmatrix}4&3 \\6&3 \end{pmatrix}$What is the sum of all the elements of the $L$ and $U$ matrices as obtained in the L U decomposition?$16$$10$$9$$6$
2 votes
1 answer
273
Test the consistency of the following system of equations$5x + 3y + 7z = 4 $$3x + 26y + 2z = 9$$7x + 2y + 10z = 5$
0 votes
1 answer
274
$1)$ How to find a matrix is diagonalizable or not?Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & -\cos\Theta \end{bmatrix}$Is it diagona...
0 votes
1 answer
275
The unique polynomial P(x) of degree 2 such that: P(1) = 1, P(3) = 27, P(4) = 64 isa) 8$x^2$ -19x + 12b) 8$x^2$ + 19x + 12c) -8$x^2$ -19x + 12d) -8$x^2$ -19x - 12
4 votes
1 answer
276
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______$a,a,a$$0,a,2a$$-a,2a,2a$$a,a+\sqrt{2},a-\sqrt{2}$
0 votes
1 answer
278
Equation of the line normal to function f(x)= $(x - 8) ^{2/3}$ +1 at P(0, 5) is(a) y = 3x -5(b) 3y = x - 15(c) 3y = x+15(d) y=3x+5
0 votes
1 answer
279
The matrix of a relation R: A->A is given by MR = Determine R-1 and compliment of R.
0 votes
1 answer
283
The number of positive integers n for which n2+96 is a perfect squareis(A) 0 (B) 1 (C) 2 (D) 4
1 votes
1 answer
284
If B has eigenvalues 1, 2, 3, C has eigenvalues 4, 5, 6, and D has eigenvalues 7, 8,9, what are the eigenvalues of the 6 by 6 matrix A =[ B C , 0 D] ?
1 votes
0 answers
285
1 votes
2 answers
288
$X$ and $Y$ are non zero square matrices of order $n \times n$, such that $XY=O$Then, which of the following options is correct?$|X| = 0$ and $|Y| \neq 0$$|X| \neq 0$ and...
1 votes
0 answers
290