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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 answered questions in Linear Algebra

0 votes
2 answers
241
ISRO 2015- Complex Numbers [EE]
If x = √ -1. then the value of x x is (a) e- π /2 (b) x (c) e π /2 (d) 1
If x = √ -1. then the value of x x is(a) e- π /2(b) x(c) e π /2(d) 1
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0 votes
2 answers
242
ISRO 2014 -Trigonometry [EE]
If tan $\Theta$ = 8 / 15 and $\Theta$ is acute, then cosec $\Theta$ (A) 8 / 17 (B) 8 / 15 (C) 17 / 8 (D) 17 / 15
If tan $\Theta$ = 8 / 15 and $\Theta$ is acute, then cosec $\Theta$(A) 8 / 17(B) 8 / 15(C) 17 / 8(D) 17 / 15
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1 votes
2 answers
243
ISRO 2013- Matrices [EE]
Characteristic roots of matrix $A$ and $A^T$ will be a) Different b) Same c) Cannot say about roots d) None of these
Characteristic roots of matrix $A$ and $A^T$ will bea) Differentb) Samec) Cannot say about rootsd) None of these
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2 votes
2 answers
244
ISRO 2013- Matrices /Mech
Tha matrix $ \begin{bmatrix} 0 & -4 &1 \\ 4& 0 &-5 \\ -1&5 &0 \end{bmatrix} $is (a) Orthogonal Matrix (b) Skew Symmetric (c) Symmetric (d) Idempotent
Tha matrix $ \begin{bmatrix} 0 & -4 &1 \\ 4& 0 &-5 \\ -1&5 &0 \end{bmatrix} $is (a) Orthogonal Matrix(b) Skew Symmetric(c) Symmetric(d) Idempotent
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2 votes
2 answers
245
ISRO 2013 - Matrices [Mech]
If A is Square Matrix of order 3, then product of A and its transpose is (a) Unit Matrix (b) Zero Matrix (c) Identity Matrix (d) Symmetric Matrix
If A is Square Matrix of order 3, then product of A and its transpose is(a) Unit Matrix(b) Zero Matrix(c) Identity Matrix(d) Symmetric Matrix
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0 votes
2 answers
246
ISRO 2006-ECE Eigen Values
The Eigen values of are: a) 6, 1 b) 6, -1 c) -6, 1 d) -6,-1
The Eigen values of are:a) 6, 1b) 6, -1c) -6, 1d) -6,-1
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0 votes
2 answers
247
ISRO 2007- ECE Matrices
The Algebraic multiplicity of the matrix A= is a) 1 b) 2 c) 3 d) 4
The Algebraic multiplicity of the matrix A= isa) 1b) 2c) 3d) 4
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0 votes
2 answers
248
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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33 votes
2 answers
249
GATE CSE 2017 Set 2 | Question: 22
Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices. Then the rank of $ P+Q$ is ___________ .
Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices.Th...
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0 votes
2 answers
250
#Testbook- 3 Qno-13
is it given correct answer ????
is it given correct answer ????
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0 votes
2 answers
252
ACE-MockTest:Matrix algebra-Rank
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1 votes
2 answers
254
MadeEasy Test Series: Linear Algebra - Eigen Value
can we use some identity to find value of ab+by+ya???without finding its eigen values and then multiplying..earlier i have read it somewhere but i forget it.
can we use some identity to find value of ab+by+ya???without finding its eigen values and then multiplying..earlier i have read it somewhere but i forget it.
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1 votes
2 answers
256
MADEEASY Doubt Matrix
If A is a Skew Symmetric MAtrix then A.A is_______ a)symmetric b)skew-symmetric c)Diagonal d)nothing can be said
If A is a Skew Symmetric MAtrix then A.A is_______a)symmetric b)skew-symmetric c)Diagonal d)nothing can be said
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2 votes
2 answers
257
GATE Overflow | Mathematics | Test 1 | Question: 23
If the determinant of an $n \times n$ matrix $A$ is zero then rank of $A$ is $n$ rank of $A\leq n-2$ $A$ has at least one zero eigen value the system of equations $Ax=0$ has no solution other than trivial solution
If the determinant of an $n \times n$ matrix $A$ is zero thenrank of $A$ is $n$rank of $A\leq n-2$$A$ has at least one zero eigen valuethe system of equations $Ax=0$ has ...
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1 votes
2 answers
259
GATE Overflow | Mathematics | Test 1 | Question: 3
$A$ is a $2\times 2$ matrix with eigenvalues $2$ and $-3$. The eigenvalues of the matrix $A^2$ are? 4,-9 2,-3 4,9 can not be determined from given data
$A$ is a $2\times 2$ matrix with eigenvalues $2$ and $-3$. The eigenvalues of the matrix $A^2$ are?4,-9 2,-3 4,9 can not be determined from given d...
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1 votes
2 answers
260
What is the minimum number of multiplications required to compute the chain of matrices?
What is the minimum number of multiplications required to compute the chain of matrices A = A1.A2.A3.A4 with size of A1 is 10x100, A2 is 100x5, A3 is 5x50, and A4 is 50x1?
What is the minimum number of multiplications required to compute the chain of matrices A = A1.A2.A3.A4 with size of A1 is 10x100, A2 is 100x5, A3 is 5x50, and A4 is 50x1...
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