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

Recent questions in Linear Algebra

0 votes
0 answers
461
Vector
https://www.youtube.com/watch?v=3SkCNpFOshk In this lecture , can somebody define in 2nd question why $X_{1}+X_{2}\notin V_{1}\cup V_{2}$? I cannot understand the proof
https://www.youtube.com/watch?v=3SkCNpFOshkIn this lecture , can somebody define in 2nd question why $X_{1}+X_{2}\notin V_{1}\cup V_{2}$?I cannot understand the proof
User Avatar
0 votes
0 answers
462
Matrix
To find the product of the non-zero eigenvalues of the matrix is ____ ... $\lambda =-1,2,0$ Where is my mistake, plz tell me
To find the product of the non-zero eigenvalues of the matrix is ____$\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ ...
User Avatar
3 votes
2 answers
463
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
0 votes
1 answer
465
ISI 2017 MMA 20
The number of the ordered pair (X, Y), where X and Y are N*N real matrices such that XY-YX=​​​​​​​​​​​​​​ I is A) 0 B) 1 C) N D) Infinite
The number of the ordered pair (X, Y), where X and Y are N*N real matrices such that XY-YX=​​​​​​​​​​​​​​ I isA) 0B) 1C) ND) Infinite
User Avatar
1 votes
2 answers
466
PGEE 2018
let $\left | A \right|=8$ ,$\left | B \right|=3$ ,$\left | C \right|=6$ then what will be value of AB$^{T}$C$^{-1}$ A) 144 B) 0 C) 4 D) 14
let $\left | A \right|=8$ ,$\left | B \right|=3$ ,$\left | C \right|=6$ then what will be value of AB$^{T}$C$^{-1}$A) 144B) 0C) 4D) 14
User Avatar
1 votes
1 answer
467
PGEE 2018
let A and B be two n*n matrices such that they follow commutative property under multiplication operation which of the following follows commutative property 1) $A^{T} B$ 2) $B^{T} A$ 3) $A^{T} B^{T}$ 4) None
let A and B be two n*n matrices such that they follow commutative property under multiplication operation which of the following follows commutative property1) $A^{T} B$2...
User Avatar
0 votes
1 answer
468
Self doubt
There are 10 different balls in such way that 6 balls are white and 4 balls are black. How many different arrangements are possible such way that black ball placed before the white ball ?
There are 10 different balls in such way that 6 balls are white and 4 balls are black. How many different arrangements are possible such way that black ball placed before...
User Avatar
1 votes
2 answers
469
linear algebra
User Avatar
0 votes
1 answer
471
Gate 2004 Question on Linear Algebra
Can Somebody Please explain me in detail description how to calculate the number of upper triangular and lower triangular of a square matrix I read somewhere that it turns out to be ((n^2)+n) /2,Can someone please provide me with a proof
Can Somebody Please explain me in detail description how to calculate the number of upper triangular and lower triangular of a square matrix I read somewhere that it turn...
User Avatar
3 votes
4 answers
472
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
10 votes
8 answers
473
ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$
Suppose the rank of the matrix$$\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$$is $2$ for some real numbers $a$ and $b$. Then $b$ equals$1$$3$$1/2$$1/3$
User Avatar
3 votes
2 answers
474
ISI2017-MMA-19
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 - px +q = 0$, then the value of the determinant $\begin{vmatrix}\alpha & \beta & \gamma\\\beta & \gamma & \alpha\\\gamma & \alpha & \beta\end{vmatrix}$ is $p$ $p^2$ $0$ $p^2+6q$
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 - px +q = 0$, then the value of the determinant$$\begin{vmatrix}\alpha & \beta & \gamma\\\beta & \gamma & \alpha\\\g...
User Avatar
8 votes
3 answers
476
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)$$\left(\dfr...
User Avatar
4 votes
1 answer
477
Made easy workbook
Let $A$ be a $4\times 4$ matrix with real entries such that $-1,1,2,-2$ are eigen values.If $B=A^4-5A^2+5I$ then trace of $A+B$ is...........
Let $A$ be a $4\times 4$ matrix with real entries such that $-1,1,2,-2$ are eigen values.If $B=A^4-5A^2+5I$ then trace of $A+B$ is...........
User Avatar
3 votes
1 answer
478
Madeeasy workbook
The number of different matrices that can be formed with elements $0,1,2,3$; each matrix having $4$ elements is $2\times 4^4$ $3\times 4^4$ $4\times 4^4$ $3\times 2^4$
The number of different matrices that can be formed with elements $0,1,2,3$; each matrix having $4$ elements is$2\times 4^4$$3\times 4^4$$4\times 4^4$$3\times 2^4$
User Avatar
1 votes
1 answer
479
Made easy Workbook
The system of equations $2x+y=5$ $x-3y=-1$ $3x+4y=k$ is consistent when $k =........$
The system of equations$2x+y=5$$x-3y=-1$$3x+4y=k$is consistent when $k =........$
User Avatar
Page: