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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 viewed questions in Linear Algebra

6 votes
6 answers
91
Gate ECE 2017 Eigen Value
For the given matrix A, one of the Eigenvalue is real $A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$ The real Eigen value is:
For the given matrix A, one of the Eigenvalue is real$A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$The ...
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2 votes
1 answer
92
matrix
If A3x3 is a matrix with |A| = 2. What is the determinant of Adj (Adj (Adj A))?
If A3x3 is a matrix with |A| = 2. What is the determinant of Adj (Adj (Adj A))?
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9 votes
2 answers
93
Mathematics: Gate 2016 EE set-2
A 3X3 matrix P is such that, P^3 = P. Then the eigenvalues of P are: 1) 1, 1, -1 2) 1, 0.5 + j0.866, 0.5 - j0.866 3) 1, -0.5 + j0.866, -0.5 - j0.866 4) 0, 1, -1
A 3X3 matrix P is such that, P^3 = P. Then the eigenvalues of P are:1) 1, 1, -12) 1, 0.5 + j0.866, 0.5 - j0.8663) 1, -0.5 + j0.866, -0.5 - j0.8664) 0, 1, -1
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2 votes
1 answer
94
What is the number of linearly independent solutions of a set of vectors taken from identity matrix?
If I have 3 sets of vectors X=(1,0,0) , Y= (0,1,0) and Z=(0,0,1) then these all form a linearly independent set of vectors ,so K(X)+P(Y)+Q(Z) =0 , so we get K=P=Q=0 , but...
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25 votes
5 answers
96
GATE CSE 2011 | Question: 40
Consider the matrix as given below. $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$ Which one of the following options provides the CORRECT values of the eigenvalues of the matrix? $1, 4, 3$ $3, 7, 3$ $7, 3, 2$ $1, 2, 3$
Consider the matrix as given below.$$\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$$Which one of the following options provides the CORRECT values of...
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1 votes
1 answer
97
Engineering Maths: Orthogonal Matrix
Is the given last point correct? But as i see in the given matrix sum of the product of first two columns (or) two rows is not zero. please verify.
Is the given last point correct?But as i see in the given matrix sum of the product of first two columns (or) two rows is not zero. please verify.
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24 votes
7 answers
98
GATE CSE 1995 | Question: 1.24
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ ... $1$ $2$ $n$ Depends on the value of $a$
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ is a real number is $$ \begin{bmatrix} 1 & a & a^2 & \dots & a^n \\ 1 & a & a^2 & \dots & a^n \\ \vdots ...
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2 votes
1 answer
100
Linear Algebra Eigenvalues
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?
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3 votes
2 answers
101
Mathematics: GATE 2016 EE SET 1
Let the eigenvalues of 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2 - 3A+4I would respectively, be (a) 2,14; x1,x2 (b) 2,14; x1+x2:x1-x2 (c) 2,0; x1, x2 (d) 2,0; x1+x2,x1-x2
Let the eigenvalues of 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2 - 3A+4I would respectivel...
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28 votes
5 answers
102
GATE CSE 2002 | Question: 5a
Obtain the eigen values of the matrix$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & -2 & 104 \\ 0 & 0 & 0 & -1 \end{bmatrix}$
Obtain the eigen values of the matrix$$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & -2 & 104 \\ 0 & 0 & 0 & -1 \end{bmatrix}$$
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17 votes
3 answers
103
GATE CSE 1994 | Question: 3.12
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
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6 votes
2 answers
104
ISRO2014-72
The rank of the matrix $A=\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$ is ______ . $0$ $1$ $2$ $3$
The rank of the matrix $A=\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$ is ______ .$0$$1$$2$$3$
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0 votes
2 answers
105
A is a 4-square matrix and A 5 = 0. Then
A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 = a) I b) -I c) 0 d) A
A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 =a) Ib) -Ic) 0d) A
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24 votes
3 answers
106
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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1 votes
1 answer
108
GATE 2012 MA Matrix
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1 votes
1 answer
110
ME: GATE-2005
A is a 3 x 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is:____________
A is a 3 x 4 real matrix and A x = b is an inconsistent system of equations. Thehighest possible rank of A is:____________
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