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

Most answered questions in Linear Algebra

10 votes
2 answers
271
ISRO2009-63
$\begin{vmatrix} 265 && 240 && 219 \\ 240 && 225 && 198 \\ 219 && 198 && 181 \\ \end{vmatrix} = $ $779$ $679$ $0$ $256$
$\begin{vmatrix} 265 && 240 && 219 \\ 240 && 225 && 198 \\ 219 && 198 && 181 \\ \end{vmatrix} = $$779$$679$$0$$256$
User Avatar
1 votes
2 answers
273
matrix
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define 4 $\times$ ... Then rank(A) equals 1 or 2 0 4 2 or 3
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define 4 $\times$ matrix A by$A = \begin{pmatrix} x_1^2+y_1^2 & x_...
User Avatar
0 votes
2 answers
275
Gate 2008 Ee
Answer given as option a ) My knowledge . Rank of a matrix Q is 4 implies 1 out of 5 rows of Q is zero linearly independent solution = n-r n--> no of unknowns r---> rank therefore linerly independent solution = 5-4 = 1 What is linerly independent Rows ... ? linerly independent vectors ?
Answer given as option a )My knowledge .Rank of a matrix Q is 4 implies 1 out of 5 rows of Q is zerolinearly independent solution = n-rn no of unknownsr - ranktherefore ...
User Avatar
0 votes
2 answers
276
GATE 2012 ME HOW TO NORMAIZE EIGEN VECTORS
User Avatar
39 votes
2 answers
277
GATE CSE 2016 Set 2 | Question: 06
Suppose that the eigenvalues of matrix $A$ are $1, 2, 4$. The determinant of $\left(A^{-1}\right)^{T}$ is _________.
Suppose that the eigenvalues of matrix $A$ are $1, 2, 4$. The determinant of $\left(A^{-1}\right)^{T}$ is _________.
User Avatar
0 votes
2 answers
278
Maths: LA Non Homogeneous Equation
Given the following set of equations: X - y - z = 0 x + y + z = 46 x - 2y +z = 16 -x - y + 2z = -7 which of the following is true ? a) no solution b) infinite many solution c) exactly one solution d) exactly one solution and atleast one of the x,y,z is negative
Given the following set of equations:X - y - z = 0x + y + z = 46x - 2y +z = 16-x - y + 2z = -7which of the following is true ?a) no solutionb) infinite many solutionc) ex...
User Avatar
0 votes
2 answers
279
Determinant of matrix
What is the determinant of matrix 2A. determinant of matrix A is 3. and IT is 4 by 4 matrix?
What is the determinant of matrix 2A. determinant of matrix A is 3. and IT is 4 by 4 matrix?
User Avatar
0 votes
2 answers
280
what is the determinant of this matrix?
Find the Determinant of $\begin{pmatrix} -4& -1 &-1 &-1 \\ -1& 2& -1& 0\\ -1& -1 & 3 & -1\\ -1 & 0&-1 & 3 \end{pmatrix}$.
Find the Determinant of $\begin{pmatrix} -4& -1 &-1 &-1 \\ -1& 2& -1& 0\\ -1& -1 & 3 & -1\\ -1 & 0&-1 & 3 \end{pmatrix}$.
User Avatar
1 votes
2 answers
282
Eigenvalues and Eigenvectors
Here answer is B. Can anyone explain this? I am confused with option A and B.
Here answer is B.Can anyone explain this? I am confused with option A and B.
User Avatar
1 votes
2 answers
283
matrix
User Avatar
3 votes
2 answers
284
Gate_2007 ME
The number of linearly independent Eigen vectors of is a) 0 b) 1 C) 2 d) infinite
The number of linearly independent Eigen vectors of is a) 0b) 1 C) 2d) infinite
User Avatar
5 votes
2 answers
286
TIFR-2015-Maths-A-6
Let $A$ be the $2 \times 2$ matrix $\begin{pmatrix} \sin\frac{\pi}{18}&-\sin \frac{4\pi}{9} \\ \sin \frac{4\pi}{9}&\sin \frac {\pi}{18} \end{pmatrix}$. Then the smallest number $n \in \mathbb{N}$ such that $A^{n}=1$ is. $3$ $9$ $18$ $27$
Let $A$ be the $2 \times 2$ matrix $\begin{pmatrix}\sin\frac{\pi}{18}&-\sin \frac{4\pi}{9} \\\sin \frac{4\pi}{9}&\sin \frac {\pi}{18}\end{pmatrix}$. Then the smallest num...
User Avatar
22 votes
2 answers
288
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
3 votes
2 answers
289
1. if V1 and V2 are eigenvectors that correspond to the distinct eigenvalues then they are linearly independent.
TRUE/FALSE :1. if V1 and V2 are eigenvectors that correspond to the distinct eigenvalues then they are linearly independent.2. if V1 and V2 are linearly independent eige...
User Avatar
Page: