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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

9 votes
2 answers
141
Mathematics: Gate 2016 EE set-2
A 3X3 matrix P is such that, P^3 = P. Then the eigenvalues of P are: 1) 1, 1, -1 2) 1, 0.5 + j0.866, 0.5 - j0.866 3) 1, -0.5 + j0.866, -0.5 - j0.866 4) 0, 1, -1
A 3X3 matrix P is such that, P^3 = P. Then the eigenvalues of P are:1) 1, 1, -12) 1, 0.5 + j0.866, 0.5 - j0.8663) 1, -0.5 + j0.866, -0.5 - j0.8664) 0, 1, -1
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9 votes
2 answers
142
ISRO2009-62
If $\text{A, B, C}$ are any three matrices, then $\text{A}'+\text{B}'+\text{C}' $ is equal to a null matrix $\text{A + B + C}$ $\text{(A + B + C)}'$ $\text{-(A + B + C})$
If $\text{A, B, C}$ are any three matrices, then $\text{A}'+\text{B}'+\text{C}' $ is equal toa null matrix$\text{A + B + C}$$\text{(A + B + C)}'$$\text{-(A + B + C})$
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9 votes
2 answers
143
ISRO2009-61
If $\begin{vmatrix} 3 && 3 \\ x && 5 \end{vmatrix} =3$ then the value of $x$ is $2$ $3$ $4$ $5$
If $\begin{vmatrix} 3 && 3 \\ x && 5 \end{vmatrix} =3$ then the value of $x$ is$2$$3$$4$$5$
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8 votes
3 answers
149
ISI2017-MMA-5
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$? $1$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{2}\right)$
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$?$1$$\left(\dfrac{1}{3}\right)$$\left(\dfrac{1}{6}\right)$$\left(\dfr...
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8 votes
4 answers
150
ISRO-DEC2017-1
Suppose $A$ is a finite set with $n$ elements.The number of elements and the rank of the largest equivalence relation on $A$ are $\{n,1\}$ $\{n,n\}$ $\{n^2,1\}$ $\{1,n^2\}$
Suppose $A$ is a finite set with $n$ elements.The number of elements and the rank of the largest equivalence relation on $A$ are$\{n,1\}$$\{n,n\}$$\{n^2,1\}$$\{1,n^2\}$
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8 votes
3 answers
153
GATE CSE 1988 | Question: 16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangular, and $P$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangula...
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8 votes
2 answers
154
ISRO2009-59
A square matrix $\text{A}$ is called orthogonal if $\text{A}'\text{A}=$ $\text{I}$ $\text{A}$ $-\text{A}$ $-\text{I}$
A square matrix $\text{A}$ is called orthogonal if $\text{A}'\text{A}=$$\text{I}$$\text{A}$$-\text{A}$$-\text{I}$
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8 votes
4 answers
155
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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