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

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

Highest voted questions in Linear Algebra

4 votes
1 answer
155
Consider the $n \times n$ matrix $M$ defined as follows:$$M=\left(\begin{array}{cccc}1 & 2 & \ldots & n \\n+1 & n+2 & \ldots & 2 n \\2 n+1 & 2 n+2 & \ldots & 3 n \\\vdots...
4 votes
1 answer
157
4 votes
1 answer
158
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______$a,a,a$$0,a,2a$$-a,2a,2a$$a,a+\sqrt{2},a-\sqrt{2}$
4 votes
2 answers
159
Nullity of a matrix = Total number columns – Rank of that matrixBut how to calculate value of x when nullity is already given(1 in this case)
4 votes
1 answer
160
4 votes
1 answer
161
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...........
4 votes
1 answer
162
A2 − A = 0, where A is a 9×9 matrix. Then (a) A must be a zero matrix (b) A is an identity matrix (c) rank of A is 1 or 0 (d) A is diagonalizablev
4 votes
1 answer
163
Assume determinant of a $3\times3$ matrix is a prime number and trace is $15.$Largest eigen value is _______(Assume only positve eigen values)
4 votes
1 answer
164
If $1,-2,3$ are the eigen values of the matrix $A$ then ratio of determinant of $B$ to the trace of $B$ is_______where $B=[adj(A)-A-A^{-1}-A^{2}]$
4 votes
0 answers
166
If $A$ and $B$ are symmetric matrices of the same order, then $AB-BA$ isNULL matrixSymmetric matrixSkew symmetric matrixOrthogonal matrix
4 votes
1 answer
167
The condition for which the eigenvalues of the matrix $A=\begin{bmatrix} 2 & 1\\ 1 &k \end{bmatrix}$ are positive is$k \frac{1}{2}$$ k −2$$ k 0$$k< \frac{-1}{2}$
4 votes
1 answer
168
If $X=\begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$, the value of $X^n$ is$\begin{bmatrix} 3n & -4n \\ n & -n \end{bmatrix}$$\begin{bmatrix} 2+n & 5-n \\ n & -n \end{bm...
4 votes
1 answer
169
if V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of Intersection of V1 and V2 is ?
4 votes
3 answers
170
In A = (aij)nxn where aij = 1 &forall; i,j then number of different independent Eigen Vectors of A are _________ . (a) 1(b) n-1(c) 2(d) n