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

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

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Recent questions in Linear Algebra

1 votes
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361
GATE 2009 MA Matrices
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3 votes
1 answer
362
GATE 2009 MA Trace
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1 votes
1 answer
363
GATE 2008 MA LU Decomposition
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1 votes
1 answer
364
GATE 2007 MA Eigen Value
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3 votes
1 answer
365
Ace test series
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366
#self doubt GATE 2018
https://gateoverflow.in/204100/gate2018-26 please explain this one in more detail!
https://gateoverflow.in/204100/gate2018-26please explain this one in more detail!
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2 votes
1 answer
367
NIELIT 2018-21
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigen vector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is $15$ $16$ $17$ $18$
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigen vector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10...
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2 votes
1 answer
368
NIELIT 2018-27
The following vectors $(1, 9, 9, 8), (2, 0, 0, 8), (2, 0, 0, 3)$ are Linearly dependent Linearly independent Constant None of these
The following vectors $(1, 9, 9, 8), (2, 0, 0, 8), (2, 0, 0, 3)$ areLinearly dependentLinearly independentConstantNone of these
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3 votes
1 answer
369
NIELIT 2018-30
If $C$ is a non-singular matrix and $B=C \begin{bmatrix} 0 & x & y \\ 0 & 0 & x \\ 0 & 0 & 0 \end{bmatrix} C^{-1}$ then: $B^2=I$ $B^2 = \text{Null Matrix}$ $B^3=I$ $B^3 = \text{Null Matrix}$
If $C$ is a non-singular matrix and $B=C \begin{bmatrix} 0 & x & y \\ 0 & 0 & x \\ 0 & 0 & 0 \end{bmatrix} C^{-1}$ then:$B^2=I$$B^2 = \text{Null Matrix}$$B^3=I$$B^3 = \te...
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1 votes
1 answer
372
Made easy workbook
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1 votes
0 answers
373
Self Doubt
Relation between rank and number of non-zero eigenvalues of a matrix If Rank of n X n matrix is r, then number of non zero eigen values ?? In either of cases det(A) = 0 or if det(A) not equal 0
Relation between rank and number of non-zero eigenvalues of a matrixIf Rank of n X n matrix is r, then number of non zero eigen values ?? In either of cases det(A) = 0 or...
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0 votes
0 answers
374
Matrices
The number of binary matrices of order $N*N$ whose determinant is exactly zero.
The number of binary matrices of order $N*N$ whose determinant is exactly zero.
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0 votes
1 answer
375
Gilbert_Strang_LU_Decomposition
For which numbers c is $A=LU$ impossible? $\begin{bmatrix} 1 & 2 &0 \\ 3 & c &1 \\ 0 &1 &1 \end{bmatrix}$
For which numbers c is $A=LU$ impossible? $\begin{bmatrix} 1 & 2 &0 \\ 3 & c &1 \\ 0 &1 &1 \end{bmatrix}$
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1 votes
0 answers
379
Linearity of Matrix
$1)$What is linearly independent solution? Why it is depend on rank of matrix? (Linearly independent solution = no of rows of matrix- rank of matrix) $I=N-R$ $2)$ Why for unique solution of a matrix , determinant of matrix need to be nonzero? What should be determinant value for infinite solution?
$1)$What is linearly independent solution? Why it is depend on rank of matrix?(Linearly independent solution = no of rows of matrix- rank of matrix) $I=N-R$ $2)$ Why for ...
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0 votes
0 answers
380
#math combat
If $A$ is $2\times 2$ matrix ,eigen value is $1,-2$ and corresponding eigen vector $[1,2]^{T}$ and $[9,1]^{T}$.find sum of element of the matrix $A.$
If $A$ is $2\times 2$ matrix ,eigen value is $1,-2$ and corresponding eigen vector $[1,2]^{T}$ and $[9,1]^{T}$.find sum of element of the matrix $A.$
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