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

Highest voted questions in Linear Algebra

3 votes
1 answer
271
GATE 2009 MA Trace
User Avatar
3 votes
1 answer
272
Ace test series
User Avatar
3 votes
1 answer
273
NIELIT 2018-30
If $C$ is a non-singular matrix and $B=C \begin{bmatrix} 0 & x & y \\ 0 & 0 & x \\ 0 & 0 & 0 \end{bmatrix} C^{-1}$ then: $B^2=I$ $B^2 = \text{Null Matrix}$ $B^3=I$ $B^3 = \text{Null Matrix}$
If $C$ is a non-singular matrix and $B=C \begin{bmatrix} 0 & x & y \\ 0 & 0 & x \\ 0 & 0 & 0 \end{bmatrix} C^{-1}$ then:$B^2=I$$B^2 = \text{Null Matrix}$$B^3=I$$B^3 = \te...
User Avatar
3 votes
1 answer
277
ISI2016-MMA-18
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then$B^2 =1$$B^2 =0$$B^2 =A$$B^2 =B$
User Avatar
3 votes
2 answers
278
Mathematics: GATE 2016 EE SET 1
Let the eigenvalues of 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2 - 3A+4I would respectively, be (a) 2,14; x1,x2 (b) 2,14; x1+x2:x1-x2 (c) 2,0; x1, x2 (d) 2,0; x1+x2,x1-x2
Let the eigenvalues of 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2 - 3A+4I would respectivel...
User Avatar
3 votes
4 answers
279
ISI-2016-04
If $a,b,c$ and $d$ satisfy the equations $a+7b+3c+5d =16$ $8a+4b+6c+2d = -16$ $2a+6b+4c+8d = 16$ $5a+3b+7c+d= -16$ Then $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$
If $a,b,c$ and $d$ satisfy the equations$a+7b+3c+5d =16$$8a+4b+6c+2d = -16$$2a+6b+4c+8d = 16$$5a+3b+7c+d= -16$Then $(a+d)(b+c)$ equals$-4$$0$$16$$-16$
User Avatar
3 votes
2 answers
280
ISI2017-MMA-19
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 - px +q = 0$, then the value of the determinant $\begin{vmatrix}\alpha & \beta & \gamma\\\beta & \gamma & \alpha\\\gamma & \alpha & \beta\end{vmatrix}$ is $p$ $p^2$ $0$ $p^2+6q$
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 - px +q = 0$, then the value of the determinant$$\begin{vmatrix}\alpha & \beta & \gamma\\\beta & \gamma & \alpha\\\g...
User Avatar
3 votes
1 answer
281
Madeeasy workbook
The number of different matrices that can be formed with elements $0,1,2,3$; each matrix having $4$ elements is $2\times 4^4$ $3\times 4^4$ $4\times 4^4$ $3\times 2^4$
The number of different matrices that can be formed with elements $0,1,2,3$; each matrix having $4$ elements is$2\times 4^4$$3\times 4^4$$4\times 4^4$$3\times 2^4$
User Avatar
3 votes
2 answers
282
Madeeasy workbook
Let $A$ be a $3\times 4$ matrix.The system of equations $Ax=0$ has unique solution Infinite solution No solution Exactly 2 solutions
Let $A$ be a $3\times 4$ matrix.The system of equations $Ax=0$ hasunique solutionInfinite solutionNo solutionExactly 2 solutions
User Avatar
3 votes
1 answer
283
matrix
Given that the matrix $A=\begin{bmatrix} 1 &2 &2 \\ 2 &1 &-2 \\ a& 2 &b \end{bmatrix}$ and $AAA^{T}=3I$ where $I$ is a $3\times3$ identity matrix$.$ Find $(a,b)$ can be$?$
Given that the matrix $A=\begin{bmatrix} 1 &2 &2 \\ 2 &1 &-2 \\ a& 2 &b \end{bmatrix}$ and $AAA^{T}=3I$ where $I$ is a $3\times3$ identity matrix$.$Find $(a,b)$ can be$?...
User Avatar
3 votes
1 answer
284
IN Gate 2007 - Matrix
Let A be an nxn real matrix such that A^2=I and y be an n-dimensional vector. Then the linear system of equations AX=Y has A) No solution B) Unique Solution C) More than one but finitely many independent solutions D) infinitely many independent solutions
Let A be an nxn real matrix such that A^2=I and y be an n-dimensional vector. Then the linear system of equations AX=Y hasA) No solutionB) Unique SolutionC) More than one...
User Avatar
3 votes
2 answers
285
Recurrance Relations
User Avatar
3 votes
0 answers
286
rank of matrix
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix. (A) Always true (B) Sometimes true (C) False (D) None of the above
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix.(A) Always true(B) ...
User Avatar
3 votes
2 answers
289
Engineering mathematics
Standard books required for linear algebra and calculus for gate syllabus ?
Standard books required for linear algebra and calculus for gate syllabus ?
User Avatar
3 votes
1 answer
290
Find the last row of the Matrix
For the first one I have got -28 and 11 as the answer but for the matrix C I am not able to get the value of element c32. c31 = c33 = 6.
For the first one I have got -28 and 11 as the answer but for the matrix C I am not able to get the value of element c32.c31 = c33 = 6.
User Avatar
Page: