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

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

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Most viewed questions in Linear Algebra

1 votes
2 answers
35
A is an upper triangular with all diagonal entries zero, then I+A is
A is an upper triangular with all diagonal entries zero, then I+A is (a) invertible       (b) idempotent (c) singular        (d) nilpotent
A is an upper triangular with all diagonal entries zero, then I+A is(a) invertible       (b) idempotent(c) singular        (d) nilpotent
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3 votes
2 answers
36
Gate_2007 ME
The number of linearly independent Eigen vectors of is a) 0 b) 1 C) 2 d) infinite
The number of linearly independent Eigen vectors of is a) 0b) 1 C) 2d) infinite
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0 votes
2 answers
39
ISRO 2010-ECE matrices
If every minor of order 'r' of a matrix 'A' is zero, then rank of 'A' is a) greater than 'r' b) equal to 'r' c) less than or equal to 'r' d) less than 'r'
If every minor of order 'r' of a matrix 'A' is zero, then rank of 'A' isa) greater than 'r'b) equal to 'r'c) less than or equal to 'r'd) less than 'r'
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35 votes
2 answers
40
GATE CSE 2014 Set 3 | Question: 5
If $V_1$ and $V_2$ are $4$-dimensional subspaces of a $6$-dimensional vector space $V$, then the smallest possible dimension of $V_1 \cap V_2$ is _____.
If $V_1$ and $V_2$ are $4$-dimensional subspaces of a $6$-dimensional vector space $V$, then the smallest possible dimension of $V_1 \cap V_2$ is _____.
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24 votes
6 answers
43
GATE CSE 2018 | Question: 17
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The larg...
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35 votes
4 answers
44
GATE CSE 2004 | Question: 27
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 exist
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...
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1 votes
3 answers
45
In a m*n order Matrix, How many submatrices are possible?
In a m*n order Matrix, How many submatrices are possible?
In a m*n order Matrix, How many submatrices are possible?
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30 votes
6 answers
47
GATE CSE 2008 | Question: 3
The following system of equations $x_1 + x_2 + 2x_3 = 1$ $x_1 + 2x_2 + 3x_3 = 2$ $x_1 + 4x_2 + αx_3 = 4$ has a unique solution. The only possible value(s) for $α$ is/are $0$ either $0$ or $1$ one of $0, 1$, or $-1$ any real number
The following system of equations$x_1 + x_2 + 2x_3 = 1$$x_1 + 2x_2 + 3x_3 = 2$$x_1 + 4x_2 + αx_3 = 4$has a unique solution. The only possible value(s) for $α$ is/are$0$...
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0 votes
3 answers
49
linear algebra
Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are (a) 1024 and−1024 (b) 1024√2 and −1024√2 (c) 4√2 and−4√2 (d) 512√2 and−512√2
Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are(a) 1024 and−1024 (b) 1024√2 and −1024√2(c...
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35 votes
4 answers
50
GATE CSE 2004 | Question: 76
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is $\leq a +b$ $\leq \max(a, b)$ $\leq \min(M-a, N-b)$ $\leq \min(a, b)$
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row ...
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