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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&0&2& 1 &0&1&0&0.83&2
\\\hline\textbf{2 Marks Count} &1&1&0& 2 &1&1&0&1&2
\\\hline\textbf{Total Marks} &3&3&2& 5 &2&3&\bf{2}&\bf{3}&\bf{5}\\\hline
\end{array}}}$$

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Recent questions in Linear Algebra

24 votes
6 answers
512
GATE CSE 2018 | Question: 17
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The larg...
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0 votes
0 answers
513
Eigen Vectors
I'm getting 2
I'm getting 2
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0 votes
0 answers
514
Matrix
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1 votes
1 answer
515
Madeeasy test series
The value of expression 385 (mod 17) in the range of 0 to 16
The value of expression 385 (mod 17) in the range of 0 to 16
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1 votes
1 answer
516
Test Series
How to solve such questions? Is there easy method? Because trial and error doesn't work.
How to solve such questions?Is there easy method?Because trial and error doesn't work.
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6 votes
1 answer
517
Made easy books GATE - 2015( IN ) 1 mark
Let $A$ be a $n\times n$ matrix with rank $ r ( 0 < r < n ) .$Then $AX = 0$ has $p$ independent solutions,where $p$ is $A)$ $r$ $B)$ $n$ $C)$ $n - r $ $D)$ $n + r$
Let $A$ be a $n\times n$ matrix with rank $ r ( 0 < r < n ) .$Then $AX = 0$ has $p$ independent solutions,where $p$ is$A)$ $r$ $B)$ $n$ $C)$ $n - r...
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1 votes
1 answer
518
Recuurence
Shouldn't the characteristic equation be (1)... But they have given (2) ... kindly help ... thanks
Shouldn't the characteristic equation be (1)... But they have given (2) ... kindly help ... thanks
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1 votes
0 answers
519
ACE test series
Answer is given as A but how B is false?
Answer is given as A but how B is false?
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1 votes
1 answer
520
Test Series ACE
How to solve? ________________ Number of non-negative integer solutions such that x+y+z=17 where x>1,y>2,z>3 is --------
How to solve?________________Number of non-negative integer solutions such thatx+y+z=17where x>1,y>2,z>3 is
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7 votes
1 answer
521
LU decomposition
In the LU decomposition of the matrix,$\begin{bmatrix} 1 &2 \\ 3 &8 \end{bmatrix}$ if the diagonal elements of $U$ are both $1$, then the trace of $L$ is$?$
In the LU decomposition of the matrix,$\begin{bmatrix} 1 &2 \\ 3 &8 \end{bmatrix}$ if the diagonal elements of $U$ are both $1$, then the trace of $L$ is$?$
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4 votes
1 answer
522
largest eigen value
Assume determinant of a $3\times3$ matrix is a prime number and trace is $15.$Largest eigen value is _______(Assume only positve eigen values)
Assume determinant of a $3\times3$ matrix is a prime number and trace is $15.$Largest eigen value is _______(Assume only positve eigen values)
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5 votes
1 answer
525
Testbook:matrix
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1 votes
0 answers
526
Linear Algebra
If $I$ is the unit matrix of order $n$ , where $k!=0$ is a constant then $adj \ kI$ is
If $I$ is the unit matrix of order $n$ , where $k!=0$ is a constant then $adj \ kI$ is
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4 votes
1 answer
527
matrix adjoint
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 $B=[adj(A)-A-A^{-1}-A^{2}]$
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 $B=[adj(A)-A-A^{-1}-A^{2}]$
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3 votes
1 answer
528
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$?...
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1 votes
0 answers
529
Matrices
$\begin{bmatrix} 1 &2 &0 \\ 1& 1 &0 \\ 2& 1 &0 \end{bmatrix}$ What is the degree sequences can we get in a graph by the above matrix
$\begin{bmatrix} 1 &2 &0 \\ 1& 1 &0 \\ 2& 1 &0 \end{bmatrix}$What is the degree sequences can we get in a graph by the above matrix
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