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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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Hot questions in Linear Algebra

18 votes
5 answers
151
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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0 votes
2 answers
152
Engineering mathematics
If A is a non-zero column matrix of order n×1 and B is a non-zero row matrix of order 1×n then rank of AB equals ? Rank(ab) can be zero???
If A is a non-zero column matrix of order n×1 and B is a non-zero row matrix of order 1×n then rank of AB equals ? Rank(ab) can be zero???
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25 votes
5 answers
153
GATE CSE 2011 | Question: 40
Consider the matrix as given below. $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$ Which one of the following options provides the CORRECT values of the eigenvalues of the matrix? $1, 4, 3$ $3, 7, 3$ $7, 3, 2$ $1, 2, 3$
Consider the matrix as given below.$$\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$$Which one of the following options provides the CORRECT values of...
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35 votes
4 answers
155
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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3 votes
1 answer
156
NIELIT 2018-30
If $C$ is a non-singular matrix and $B=C \begin{bmatrix} 0 & x & y \\ 0 & 0 & x \\ 0 & 0 & 0 \end{bmatrix} C^{-1}$ then: $B^2=I$ $B^2 = \text{Null Matrix}$ $B^3=I$ $B^3 = \text{Null Matrix}$
If $C$ is a non-singular matrix and $B=C \begin{bmatrix} 0 & x & y \\ 0 & 0 & x \\ 0 & 0 & 0 \end{bmatrix} C^{-1}$ then:$B^2=I$$B^2 = \text{Null Matrix}$$B^3=I$$B^3 = \te...
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0 votes
0 answers
157
Linear Algebra, Vectors
What is the equation of the plane that contains point (-2, 4, 5) and the vector (7, 0, -6) is normal to the plane? And check if this plane intersects the y-axis.
What is the equation of the plane that contains point (-2, 4, 5) and the vector (7, 0, -6) is normal to the plane? And check if this plane intersects the y-axis.
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0 votes
0 answers
158
Linear Algebra, Vectors
Find equation of a line passes through the points = (0, 1, 2) and = (-1, 1, 1).
Find equation of a line passes through the points = (0, 1, 2) and = (-1, 1, 1).
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2 votes
2 answers
163
Linear algebra
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? (a) [ 3 −2 1 ] (b) [ −3 2 −1 ] (c) [ 1 −2 3 ] (d) [ 5 2 0 ]
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...
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0 votes
0 answers
164
Self Doubt
Question: How NullSpace of the matrix A and the uniqueness of the solution of Ax=b are related ??
Question: How NullSpace of the matrix A and the uniqueness of the solution of Ax=b are related ??
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1 votes
0 answers
165
DRDO CSE 2022 Paper 1 | Question: 2
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where \[M=\left[\begin{array}{cc} 4 & 5 \\ 2 & -5 \end{array}\right].\]
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where\[M=\left[\begin{array}{cc}4 & 5 \\2 & -5\end{array}\right].\]
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0 votes
1 answer
166
Testbook Test Series
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0 votes
1 answer
167
NPTEL Assignment Question
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35 votes
4 answers
169
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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0 votes
0 answers
170
#LinearAlgebra
Is this correct? ​​​​​
Is this correct?​​​​​
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