Register

Web Page

Syllabus: Matrices, determinants, System of linear equations, Eigenvalues and eigenvectors, LU decomposition.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &0&1&0&1&1&1&1&1&2&0&0.9&2
\\\hline\textbf{2 Marks Count} & 2 &1&1&1&1&1&2&1&0&0&0&1&2
\\\hline\textbf{Total Marks} & 5 &2&3&2&3&3&5&3&1&2&\bf{1}&\bf{2.9}&\bf{5}\\\hline
\end{array}}}$$

Filter

Hot questions in Linear Algebra

3 votes
1 answer
342
TIFR CSE 2016 | Part A | Question: 3
Consider the following set of $3n$ linear equations in $3n$ ... $\mathbb{R}^{3n}$ of dimension n $S$ is a subspace of $\mathbb{R}^{3n}$ of dimension $n-1$ $S$ has exactly $n$ elements
Consider the following set of $3n$ linear equations in $3n$ variables:$\begin{matrix} x_1-x_2=0 & x_4-x_5 =0 & \dots & x_{3n-2}-x_{3n-1}=0 \\ x_2-x_3=0 & x_5-x_6=0 & & x_...
User Avatar
21 votes
3 answers
344
GATE CSE 2005 | Question: 49
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$ $-1$ and $1$ $1$ and $6$ $2$ and $5$ $4$ and $-1$
What are the eigenvalues of the following $2\times 2$ matrix? $$\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$$-1$ and $1$$1$ and $6$$2$ and $5$$4$ and $-1$...
User Avatar
1 votes
1 answer
346
ISI2015-MMA-37
Let $a$ be a non-zero real number. Define $f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$ for $x \in \mathbb{R}$. Then, the number of distinct real roots of $f(x) =0$ is $1$ $2$ $3$ $4$
Let $a$ be a non-zero real number. Define$$f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$$ for $x \in \mathbb{R}$....
User Avatar
0 votes
2 answers
347
ISRO 2010-ECE matrices
If every minor of order 'r' of a matrix 'A' is zero, then rank of 'A' is a) greater than 'r' b) equal to 'r' c) less than or equal to 'r' d) less than 'r'
If every minor of order 'r' of a matrix 'A' is zero, then rank of 'A' isa) greater than 'r'b) equal to 'r'c) less than or equal to 'r'd) less than 'r'
User Avatar
22 votes
2 answers
349
TIFR CSE 2012 | Part B | Question: 12
Let $A$ be a matrix such that $A^{k}=0$. What is the inverse of $I - A$? $0$ $I$ $A$ $1 + A + A^{2} + ...+ A^{k - 1}$ Inverse is not guaranteed to exist.
Let $A$ be a matrix such that $A^{k}=0$. What is the inverse of $I - A$?$0$$I$$A$$1 + A + A^{2} + ...+ A^{k - 1}$Inverse is not guaranteed to exist.
User Avatar
1 votes
1 answer
350
ISI2017-DCG-25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is $\pi$ $\frac{\pi}{2}$ $0$ $1$
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [...
User Avatar
3 votes
1 answer
352
ISI2014-DCG-38
Suppose that $A$ is a $3 \times 3$ real matrix such that for each $u=(u_1, u_2, u_3)’ \in \mathbb{R}^3, \: u’Au=0$ where $u’$ stands for the transpose of $u$. Then which one of the following is true? $A’=-A$ $A’=A$ $AA’=I$ None of these
Suppose that $A$ is a $3 \times 3$ real matrix such that for each $u=(u_1, u_2, u_3)’ \in \mathbb{R}^3, \: u’Au=0$ where $u’$ stands for the transpose of $u$. Then ...
User Avatar
0 votes
1 answer
355
characteristics polynomial
A is 5×5 matrix, all of whose entries are 1, then (a) A is not diagonalizable (b) A is idempotent (c) A is nilpotent (d) The minimal polynomial and the characteristics polynomial of A are not equal
A is 5×5 matrix, all of whose entries are 1, then(a) A is not diagonalizable(b) A is idempotent(c) A is nilpotent(d) The minimal polynomial and the characteristics polyn...
User Avatar
6 votes
6 answers
357
Gate ECE 2017 Eigen Value
For the given matrix A, one of the Eigenvalue is real $A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$ The real Eigen value is:
For the given matrix A, one of the Eigenvalue is real$A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$The ...
User Avatar
0 votes
2 answers
358
A is a 4-square matrix and A 5 = 0. Then
A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 = a) I b) -I c) 0 d) A
A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 =a) Ib) -Ic) 0d) A
User Avatar
1 votes
1 answer
359
ISI2014-DCG-64
The value of $\lambda$ such that the system of equation $\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & -4 \\ x & + & y & + & \lambda z & = & 4 \end{array}$ has no solution is $3$ $1$ $0$ $-3$
The value of $\lambda$ such that the system of equation$$\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & -4 \\ x & + & y & + & \lambda z & = &...
User Avatar
Page: