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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&0&2& 1 &0&1&0&0.83&2
\\\hline\textbf{2 Marks Count} &1&1&0& 2 &1&1&0&1&2
\\\hline\textbf{Total Marks} &3&3&2& 5 &2&3&\bf{2}&\bf{3}&\bf{5}\\\hline
\end{array}}}$$

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Highest voted questions in Linear Algebra

18 votes
2 answers
81
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 20
Consider Three matrices $A, B$ and $C$ ... $\alpha_1$, then: The Entries which are not shown in matrices are zeros. What is the rank of $B ?$
Consider Three matrices $A, B$ and $C$ such that -$$\underbrace{\left(\begin{array}{lllll}1 & 2 & 4 & 2 & 5 \\& 2 & 3 & 5 & 6 \\& & 3 & 4 & 3 \\& & & 4 & 3 \\& & & 5\end{...
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18 votes
5 answers
85
GATE CSE 2021 Set 1 | Question: 52
Consider the following matrix.$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$The largest eigenvalue of the above matrix is __________.
Consider the following matrix.$$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$$The largest eigenvalue of the above matrix is __...
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18 votes
3 answers
87
GATE CSE 1987 | Question: 1-xxiii
A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above
A square matrix is singular whenever The rows are linearly independentThe columns are linearly independentThe row are linearly dependentNone of the above
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18 votes
4 answers
88
GATE CSE 1994 | Question: 1.9
The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is: $0$ $1$ $2$ $3$
The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is:$0$$1$$2$$3$
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18 votes
5 answers
89
GATE CSE 1997 | Question: 1.3
The determinant of the matrix $\begin{bmatrix} 6 & -8 & 1 & 1 \\ 0 & 2 & 4 & 6 \\ 0 & 0 & 4 & 8 \\ 0 & 0 & 0 & -1 \end{bmatrix}$ $11$ $-48$ $0$ $-24$
The determinant of the matrix $\begin{bmatrix} 6 & -8 & 1 & 1 \\ 0 & 2 & 4 & 6 \\ 0 & 0 & 4 & 8 \\ 0 & 0 & 0 & -1 \end{bmatrix}$$11$$-48$$0$$-24$
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17 votes
3 answers
95
GATE CSE 1994 | Question: 3.12
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
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16 votes
2 answers
96
GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 1
Consider the vectors $\mathbf{v}_1$ and $\mathbf{v}_2$ ... otherwise The vectors $\left\{\mathbf{v}_1, \mathbf{v}_2\right\}$ are linearly independent when $t=4$, and linearly dependent otherwise
Consider the vectors $\mathbf{v}_1$ and $\mathbf{v}_2$ given by$$\mathbf{v}_1=\left(\begin{array}{l}2 \\t \\3\end{array}\right), \quad \mathbf{v}_2=\left(\begin{array}{l}...
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16 votes
5 answers
97
GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 11
Which of the following is(are) true for the following system of linear equations $\text{AX}=\overrightarrow{0}$ ... $\text{AX}=\overrightarrow{0}$.
Which of the following is(are) true for the following system of linear equations $\text{AX}=\overrightarrow{0}$$$\left[\begin{array}{ccc}2 & 3 & -5 \\-5 & -1 & 32 \\2 & -...
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16 votes
3 answers
98
GATE CSE 2002 | Question: 1.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is$4$$2$$1$$0$
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