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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

0 votes
2 answers
663
How to solve this Determinant question
2a1b1 a1b2+a2b1 a1b3+a3b1 a1b2+a2b1 2a2b2 a2b3+a3b1 a1b3+a3b1 a3b2+a2b3 2a3b3 Express this 3x3 determinant as product of 2 determinants and find it's value
2a1b1a1b2+a2b1a1b3+a3b1a1b2+a2b12a2b2a2b3+a3b1a1b3+a3b1a3b2+a2b32a3b3Express this 3x3 determinant as product of 2 determinants and find it's value
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0 votes
1 answer
665
use of calculator
Can we use calculator provided in exam to find out determinant?
Can we use calculator provided in exam to find out determinant?
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0 votes
2 answers
666
Question regarding symmetric matrix
Is every square matrix a symmetric matrix? Or Is every square DIAGONAL matrix is a symmetric matrix? Please tell which statement is true?
Is every square matrix a symmetric matrix?OrIs every square DIAGONAL matrix is a symmetric matrix?Please tell which statement is true?
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9 votes
2 answers
667
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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1 votes
2 answers
671
Test by Bikram | Mock GATE | Test 4 | Question: 1
The sum of the diagonal elements of a $ 2\times 2 $ upper triangular matrix is $-6.$ Then, the maximum possible value of the determinant of the matrix is ________.
The sum of the diagonal elements of a $ 2\times 2 $ upper triangular matrix is $-6.$ Then, the maximum possible value of the determinant of the matrix is ________.
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1 votes
1 answer
672
Matrices
Let $\begin{pmatrix} -1 &2 \\ 0 & -1 \end{pmatrix}$,and $B=A+A^{2}+A^{3}+\dots +A^{50}$, then $B^{2}=I$ $B^{2}=0$ $B^{2}=A$ $B^{2}=B$
Let $\begin{pmatrix} -1 &2 \\ 0 & -1 \end{pmatrix}$,and $B=A+A^{2}+A^{3}+\dots +A^{50}$, then$B^{2}=I$ $B^{2}=0$ $B^{2}=A$ $B^{2}=B$...
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11 votes
3 answers
673
ISRO2017-1
If $\text{A}$ is a skew symmetric matrix then $\text{A}^t$ is Diagonal matrix $\text{A}$ $0$ $-\text{A}$
If $\text{A}$ is a skew symmetric matrix then $\text{A}^t$ isDiagonal matrix $\text{A}$$0$$-\text{A}$
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0 votes
0 answers
674
Linear algebra
Which book to study for Linear algebra grewal or Gilbert Strang from gate perspective?
Which book to study for Linear algebra grewal or Gilbert Strang from gate perspective?
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2 votes
1 answer
675
ISI Sample Paper Question
Let A be a square matrix such that $A^{3}$ = 0, but $A^{2} \neq 0$. Then which of the following statements is not necessarily true? (A) $A \neq A^{2}$ (B) Eigenvalues of $A^{2}$ are all zero (C) rank(A) > rank($A^{2}$ ) (D) rank(A) > trace(A)
Let A be a square matrix such that $A^{3}$ = 0, but $A^{2} \neq 0$. Then which of the following statements is not necessarily true?(A) $A \neq A^{2}$(B) Eigenvalues of $A...
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1 votes
1 answer
676
Gilbert Strang Problem set 1.3
Choose a coefficient b that makes this system singular. Then choose a right-hand side g that makes it solvable. Find two solutions in that singular case. $2x +by = 16$ $4x + 8y = g$
Choose a coefficient b that makes this system singular. Then choose a right-hand side g that makes it solvable. Find two solutions in that singular case. $2x ...
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0 votes
1 answer
677
linear algebra
STATE TRUE OR FALSE cofactor and minor of an element in a matrix exists if and only if that matrix is a square matrix.
STATE TRUE OR FALSEcofactor and minor of an element in a matrix exists if and only if that matrix is a square matrix.
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0 votes
1 answer
678
The number of positive integers n for which n2+96 is a perfect square is
The number of positive integers n for which n2+96 is a perfect square is (A) 0 (B) 1 (C) 2 (D) 4
The number of positive integers n for which n2+96 is a perfect squareis(A) 0 (B) 1 (C) 2 (D) 4
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0 votes
2 answers
680
linear algebra
Let A and B be two matrices.Which of the following statements is TRUE ? S1 : If product of A and B ( (i.e) AB ) = 0-matrix ,then either one of A or B should be equal to 0-matrix. S2 : If product of A and B ( (i.e) AB ) = A , then B should be an identity matrix.
Let A and B be two matrices.Which of the following statements is TRUE ? S1 : If product of A and B ( (i.e) AB ) = 0-matrix ,then either one of A or B should be equa...
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