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

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

Hot questions in Linear Algebra

0 votes
1 answer
331
The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________
2 votes
1 answer
332
If the system of equations$\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$with $a,b,c \neq 1$ has a non trivial solutions, the value of $$\frac{1}{...
4 votes
1 answer
333
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______$a,a,a$$0,a,2a$$-a,2a,2a$$a,a+\sqrt{2},a-\sqrt{2}$
0 votes
1 answer
334
45 votes
3 answers
335
Let $A$ be an $n \times n$ matrix of the following form.$$A = \begin{bmatrix}3&1&0&0&0&\ldots&0&0&0\\1&3&1&0&0&\ldots&0&0&0\\0&1&3&1&0&\ldots&0&0&0\\0&0&1&3&1&\ldots&0&0&...
1 votes
1 answer
336
Is the answer and explaination given correct ?
35 votes
2 answers
337
If $V_1$ and $V_2$ are $4$-dimensional subspaces of a $6$-dimensional vector space $V$, then the smallest possible dimension of $V_1 \cap V_2$ is _____.
3 votes
1 answer
338
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then$B^2 =1$$B^2 =0$$B^2 =A$$B^2 =B$
6 votes
3 answers
340
If $C$ is a skew-symmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is ascalar matrixnull matrixunit matrixmatrix will all elements $1$
1 votes
1 answer
341
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alp...
0 votes
0 answers
342
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
12 votes
2 answers
344
A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is:$\frac{1}{\sqrt{3}} (i+j+k)$$\frac{1}{3} (i+j-k)$$\frac{1}{3} (i-j-k)$$\frac{1}{\sqrt{3}} (i...
1 votes
2 answers
345
0 votes
0 answers
346
The ans given is b, but i am not able to understande why. According to me the largest eigen value is 2, and therefore none of the option matches..!
0 votes
1 answer
347
1 votes
2 answers
348
If the entries in each column of a square matrix M add up to 1, then an eigen value of M isA) 4 B) 3 C) 2 D) 1
16 votes
3 answers
349
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is$4$$2$$1$$0$