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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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Recent questions in Linear Algebra

8 votes
4 answers
741
ISRO2008-34
If a square matrix A satisfies $A^TA=I$, then the matrix $A$ is Idempotent Symmetric Orthogonal Hermitian
If a square matrix A satisfies $A^TA=I$, then the matrix $A$ isIdempotentSymmetricOrthogonalHermitian
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5 votes
3 answers
742
ISRO2007-09
Eigen vectors of $\begin{bmatrix} 1 && \cos \theta \\ \cos \theta && 1 \end{bmatrix}$ are $\begin{bmatrix} a^n && 1 \\ 0 && a^n \end{bmatrix}$ $\begin{bmatrix} a^n && n \\ 0 && a^n \end{bmatrix}$ ... $\begin{bmatrix} a^n && na^{n-1} \\ -n && a^n \end{bmatrix}$
Eigen vectors of $\begin{bmatrix} 1 && \cos \theta \\ \cos \theta && 1 \end{bmatrix}$ are$\begin{bmatrix} a^n && 1 \\ 0 && a^n \end{bmatrix}$$\begin{bmatrix} a^n && n \\ ...
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0 votes
1 answer
743
IISC-CSA-Research-Test-1
What is the determinant of the following matrix? $\begin{matrix} 76 && 18 && 34 \\ 14 && 12 && 6 \\ 90 && 30 && 40 \end{matrix}$
What is the determinant of the following matrix?$\begin{matrix} 76 && 18 && 34 \\ 14 && 12 && 6 \\ 90 && 30 && 40 \end{matrix}$
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2 votes
1 answer
744
1000th power of a matrix
Find the 1000_th power of the matrix -
Find the 1000_th power of the matrix -
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10 votes
2 answers
745
ISRO2009-63
$\begin{vmatrix} 265 && 240 && 219 \\ 240 && 225 && 198 \\ 219 && 198 && 181 \\ \end{vmatrix} = $ $779$ $679$ $0$ $256$
$\begin{vmatrix} 265 && 240 && 219 \\ 240 && 225 && 198 \\ 219 && 198 && 181 \\ \end{vmatrix} = $$779$$679$$0$$256$
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1 votes
2 answers
747
matrix
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define 4 $\times$ ... Then rank(A) equals 1 or 2 0 4 2 or 3
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define 4 $\times$ matrix A by$A = \begin{pmatrix} x_1^2+y_1^2 & x_...
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1 votes
1 answer
749
Linear Algebra \ determinant
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1 votes
1 answer
750
Find the Eigen Vector
Find the Eigenvector of $\begin{bmatrix} 1 & cos\theta\\ cos \theta & 1 \end{bmatrix}$
Find the Eigenvector of $\begin{bmatrix} 1 & cos\theta\\ cos \theta & 1 \end{bmatrix}$
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1 votes
1 answer
752
matrix doubt
which of the above is true?
which of the above is true?
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11 votes
3 answers
753
ISI2016
Let $A$ be a matrix such that: $A=\begin{pmatrix} -1 & 2\\ 0 & -1 \end{pmatrix}$ and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true? $B^{2}=I$ $B^{2}=0$ $B^{2}=B$ None of the above
Let $A$ be a matrix such that:$A=\begin{pmatrix} -1 & 2\\ 0 & -1 \end{pmatrix}$and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true?$B^{2}=I$$B^{2}=0$$B^...
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0 votes
2 answers
756
Gate 2008 Ee
Answer given as option a ) My knowledge . Rank of a matrix Q is 4 implies 1 out of 5 rows of Q is zero linearly independent solution = n-r n--> no of unknowns r---> rank therefore linerly independent solution = 5-4 = 1 What is linerly independent Rows ... ? linerly independent vectors ?
Answer given as option a )My knowledge .Rank of a matrix Q is 4 implies 1 out of 5 rows of Q is zerolinearly independent solution = n-rn no of unknownsr - ranktherefore ...
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0 votes
2 answers
757
GATE 2012 ME HOW TO NORMAIZE EIGEN VECTORS
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1 votes
1 answer
758
Gate 2013 IN What do you mean by dimension of null space?
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0 votes
0 answers
759
Gate 2014 IN
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0 votes
1 answer
760
Gate 2015 EE
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