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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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Most answered questions in Linear Algebra

11 votes
3 answers
121
ISRO2017-1
If $\text{A}$ is a skew symmetric matrix then $\text{A}^t$ is Diagonal matrix $\text{A}$ $0$ $-\text{A}$
If $\text{A}$ is a skew symmetric matrix then $\text{A}^t$ isDiagonal matrix $\text{A}$$0$$-\text{A}$
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1 votes
3 answers
122
ISRO 2015- Eigen Values [mech]
$\begin{bmatrix} 4 & 1 \\ 1& 4 \end{bmatrix}$ Eigen values of the matrix are: a) 3,-3 b) -3, -5 c) 3, 5 d) 5 ,0
$\begin{bmatrix} 4 & 1 \\ 1& 4 \end{bmatrix}$Eigen values of the matrix are:a) 3,-3b) -3, -5c) 3, 5d) 5 ,0
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0 votes
3 answers
123
ISRO 2006-ECE Matrix determinant
The determinant of is: a) 0 b) -1 c) 1 d) 2
The determinant of is:a) 0b) -1c) 1d) 2
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1 votes
3 answers
124
ISRO2012-ECE: Engineering Mathematics
The system of equations $x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8$ has A unique solution No solution An infinite number of solutions None of these
The system of equations $x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8$ hasA unique solutionNo solutionAn infinite number of solutionsNone of these
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8 votes
3 answers
125
GATE CSE 1988 | Question: 16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangular, and $P$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangula...
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18 votes
3 answers
126
GATE CSE 1987 | Question: 1-xxiii
A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above
A square matrix is singular whenever The rows are linearly independentThe columns are linearly independentThe row are linearly dependentNone of the above
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5 votes
3 answers
127
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}$$\begin{bmatrix} a^n && n \\ ...
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11 votes
3 answers
128
ISI2016
Let $A$ be a matrix such that: $A=\begin{pmatrix} -1 & 2\\ 0 & -1 \end{pmatrix}$ and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true? $B^{2}=I$ $B^{2}=0$ $B^{2}=B$ None of the above
Let $A$ be a matrix such that:$A=\begin{pmatrix} -1 & 2\\ 0 & -1 \end{pmatrix}$and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true?$B^{2}=I$$B^{2}=0$$B^...
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1 votes
3 answers
129
In a m*n order Matrix, How many submatrices are possible?
In a m*n order Matrix, How many submatrices are possible?
In a m*n order Matrix, How many submatrices are possible?
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4 votes
3 answers
130
different independent eigen vectors
In A = (aij)nxn where aij = 1 ∀ i,j then number of different independent Eigen Vectors of A are _________ . (a) 1 (b) n-1 (c) 2 (d) n
In A = (aij)nxn where aij = 1 ∀ i,j then number of different independent Eigen Vectors of A are _________ . (a) 1(b) n-1(c) 2(d) n
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4 votes
3 answers
131
eigen value
Eigenvalue of matrix $A$ , $\begin{bmatrix} 2 &7 &10 \\ 5& 2 & 25\\ 1& 6 &5 \end{bmatrix}$ is $-9.33$ other eigenvalue is 1) $18.33$ 2) $-18.33$ 3) $18.33-9.33 i$ 4) $18.33+9.33i$
Eigenvalue of matrix $A$ , $\begin{bmatrix} 2 &7 &10 \\ 5& 2 & 25\\ 1& 6 &5 \end{bmatrix}$ is $-9.33$ other eigenvalue is1) $18.3...
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24 votes
3 answers
132
TIFR CSE 2013 | Part B | Question: 3
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant? Hint: Use modulo $2$ arithmetic. $20160$ $32767$ $49152$ $57343$ $65520$
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant?Hint: Use modulo $2$ arithmetic.$20160$$32767$$49152$$57343$$65520$
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23 votes
3 answers
133
GATE CSE 2015 Set 2 | Question: 5
The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.
The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.
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45 votes
3 answers
134
GATE IT 2004 | Question: 32
Let $A$ be an $n \times n$ ...
Let $A$ be an $n \times n$ matrix of the following form.$$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&...
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17 votes
3 answers
135
GATE CSE 1994 | Question: 3.12
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
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26 votes
3 answers
136
GATE CSE 1994 | Question: 1.2
Let $A$ and $B$ be real symmetric matrices of size $n \times n$. Then which one of the following is true? $AA'=I$ $A=A^{-1}$ $AB=BA$ $(AB)'=BA$
Let $A$ and $B$ be real symmetric matrices of size $n \times n$. Then which one of the following is true?$AA'=I$$A=A^{-1}$$AB=BA$$(AB)'=BA$
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22 votes
3 answers
138
GATE CSE 1998 | Question: 1.2
Consider the following set of equations $x+2y=5$ $4x+8y=12$ $3x+6y+3z=15$ This set has unique solution has no solution has finite number of solutions has infinite number of solutions
Consider the following set of equations$x+2y=5$$4x+8y=12$$3x+6y+3z=15$This sethas unique solutionhas no solutionhas finite number of solutionshas infinite number of solut...
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21 votes
3 answers
139
GATE CSE 2005 | Question: 49
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$ $-1$ and $1$ $1$ and $6$ $2$ and $5$ $4$ and $-1$
What are the eigenvalues of the following $2\times 2$ matrix? $$\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$$-1$ and $1$$1$ and $6$$2$ and $5$$4$ and $-1$...
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16 votes
3 answers
140
GATE CSE 2002 | Question: 1.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is$4$$2$$1$$0$
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