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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
2 answers
801
What is the minimum number of multiplications required to compute the chain of matrices?
What is the minimum number of multiplications required to compute the chain of matrices A = A1.A2.A3.A4 with size of A1 is 10x100, A2 is 100x5, A3 is 5x50, and A4 is 50x1?
What is the minimum number of multiplications required to compute the chain of matrices A = A1.A2.A3.A4 with size of A1 is 10x100, A2 is 100x5, A3 is 5x50, and A4 is 50x1...
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1 votes
1 answer
802
Eigen values
To find out the Eigen values we put the |A-⋋I | =0 why we put the determinant =0 . Is there any specific reason For this
To find out the Eigen values we put the |A-⋋I | =0 why we put the determinant =0 .Is there any specific reason For this
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1 votes
1 answer
803
Eigen values and EigenVector
can anyone explain me how to find matrix if eigenvector and eigenvalues are given how to find eigenvalue when eigenvector and matrix is given how to find eigenvector when eigenvalue and matrix is given totally confused in this thing please explain with example
can anyone explain me how to find matrix if eigenvector and eigenvalues are givenhow to find eigenvalue when eigenvector and matrix is givenhow to find eigenvector when ...
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1 votes
1 answer
805
linear system of equations (Non homogeneous system of equations)
x1 + 2x2 + x3 +4x4 = 2 3x1 + 6x2 + 3x3 + 12x4 = 6 For the above set of equation find it is has no solution unique solution trivial solution multiple non trivial solution
x1 + 2x2 + x3 +4x4 = 23x1 + 6x2 + 3x3 + 12x4 = 6For the above set of equation find it is hasno solutionunique solutiontrivial solutionmultiple non trivial solution
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0 votes
1 answer
806
GATE DISCRETE MATHS
The matrix of a relation R: A->A is given by MR = Determine R-1 and compliment of R.
The matrix of a relation R: A->A is given by MR = Determine R-1 and compliment of R.
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4 votes
1 answer
807
Power Matrix
If $X=\begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$, the value of $X^n$ is $\begin{bmatrix} 3n & -4n \\ n & -n \end{bmatrix}$ $\begin{bmatrix} 2+n & 5-n \\ n & -n \end{bmatrix}$ $\begin{bmatrix} 3^n & (-4)^n \\ 1^n & (-1)^n \end{bmatrix}$ None of the above
If $X=\begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$, the value of $X^n$ is$\begin{bmatrix} 3n & -4n \\ n & -n \end{bmatrix}$$\begin{bmatrix} 2+n & 5-n \\ n & -n \end{bm...
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6 votes
2 answers
808
ISRO2014-72
The rank of the matrix $A=\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$ is ______ . $0$ $1$ $2$ $3$
The rank of the matrix $A=\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$ is ______ .$0$$1$$2$$3$
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10 votes
2 answers
809
ISRO2011-36
If $\text{A}$ and $\text{B}$ are square matrices with same order and $\text{A}$ is symmetric, then $\text{B}^{\text{T}}\text{AB}$ is Skew symmetric Symmetric Orthogonal Idempotent
If $\text{A}$ and $\text{B}$ are square matrices with same order and $\text{A}$ is symmetric, then $\text{B}^{\text{T}}\text{AB}$ isSkew symmetricSymmetricOrthogonalIdemp...
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9 votes
2 answers
810
ISRO2009-62
If $\text{A, B, C}$ are any three matrices, then $\text{A}'+\text{B}'+\text{C}' $ is equal to a null matrix $\text{A + B + C}$ $\text{(A + B + C)}'$ $\text{-(A + B + C})$
If $\text{A, B, C}$ are any three matrices, then $\text{A}'+\text{B}'+\text{C}' $ is equal toa null matrix$\text{A + B + C}$$\text{(A + B + C)}'$$\text{-(A + B + C})$
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9 votes
2 answers
811
ISRO2009-61
If $\begin{vmatrix} 3 && 3 \\ x && 5 \end{vmatrix} =3$ then the value of $x$ is $2$ $3$ $4$ $5$
If $\begin{vmatrix} 3 && 3 \\ x && 5 \end{vmatrix} =3$ then the value of $x$ is$2$$3$$4$$5$
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11 votes
2 answers
812
ISRO2009-60
If two adjacent rows of a determinant are interchanged, the value of the determinant becomes zero remains unaltered becomes infinitive becomes negative of its original value
If two adjacent rows of a determinant are interchanged, the value of the determinantbecomes zeroremains unalteredbecomes infinitivebecomes negative of its original value
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8 votes
2 answers
813
ISRO2009-59
A square matrix $\text{A}$ is called orthogonal if $\text{A}'\text{A}=$ $\text{I}$ $\text{A}$ $-\text{A}$ $-\text{I}$
A square matrix $\text{A}$ is called orthogonal if $\text{A}'\text{A}=$$\text{I}$$\text{A}$$-\text{A}$$-\text{I}$
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8 votes
4 answers
814
ISRO2008-34
If a square matrix A satisfies $A^TA=I$, then the matrix $A$ is Idempotent Symmetric Orthogonal Hermitian
If a square matrix A satisfies $A^TA=I$, then the matrix $A$ isIdempotentSymmetricOrthogonalHermitian
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5 votes
3 answers
815
ISRO2007-09
Eigen vectors of $\begin{bmatrix} 1 && \cos \theta \\ \cos \theta && 1 \end{bmatrix}$ are $\begin{bmatrix} a^n && 1 \\ 0 && a^n \end{bmatrix}$ $\begin{bmatrix} a^n && n \\ 0 && a^n \end{bmatrix}$ ... $\begin{bmatrix} a^n && na^{n-1} \\ -n && a^n \end{bmatrix}$
Eigen vectors of $\begin{bmatrix} 1 && \cos \theta \\ \cos \theta && 1 \end{bmatrix}$ are$\begin{bmatrix} a^n && 1 \\ 0 && a^n \end{bmatrix}$$\begin{bmatrix} a^n && n \\ ...
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0 votes
1 answer
816
IISC-CSA-Research-Test-1
What is the determinant of the following matrix? $\begin{matrix} 76 && 18 && 34 \\ 14 && 12 && 6 \\ 90 && 30 && 40 \end{matrix}$
What is the determinant of the following matrix?$\begin{matrix} 76 && 18 && 34 \\ 14 && 12 && 6 \\ 90 && 30 && 40 \end{matrix}$
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2 votes
1 answer
817
1000th power of a matrix
Find the 1000_th power of the matrix -
Find the 1000_th power of the matrix -
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10 votes
2 answers
818
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$
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1 votes
2 answers
820
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_...
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