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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

45 votes
3 answers
61
GATE IT 2004 | Question: 32
Let $A$ be an $n \times n$ ...
Let $A$ be an $n \times n$ matrix of the following form.$$A = \begin{bmatrix}3&1&0&0&0&\ldots&0&0&0\\1&3&1&0&0&\ldots&0&0&0\\0&1&3&1&0&\ldots&0&0&0\\0&0&1&3&1&\ldots&0&0&...
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26 votes
3 answers
62
GATE CSE 1994 | Question: 1.2
Let $A$ and $B$ be real symmetric matrices of size $n \times n$. Then which one of the following is true? $AA'=I$ $A=A^{-1}$ $AB=BA$ $(AB)'=BA$
Let $A$ and $B$ be real symmetric matrices of size $n \times n$. Then which one of the following is true?$AA'=I$$A=A^{-1}$$AB=BA$$(AB)'=BA$
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23 votes
3 answers
63
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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2 votes
1 answer
65
How to prove Rank(AB) <= min(Rank(A),Rank(B)) ?
Given A and B are matrices such that they can be multiplied. How to prove Rank(AB) ≤ min(Rank(A),Rank(B)) ?
Given A and B are matrices such that they can be multiplied.How to prove Rank(AB) ≤ min(Rank(A),Rank(B)) ?
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26 votes
8 answers
66
GATE IT 2006 | Question: 26
What are the eigenvalues of the matrix $P$ given below $P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$ $a, a -√2, a + √2$ $a, a, a$ $0, a, 2a$ $-a, 2a, 2a$
What are the eigenvalues of the matrix $P$ given below$$P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$$ $a, a -√2, a + √2...
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26 votes
5 answers
68
GATE CSE 1998 | Question: 2.2
Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$ Which of the following is a factor of $\Delta$? $a+b$ $a-b$ $a+b+c$ $abc$
Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$Which of the following is a factor of $\Delta$?$a+b$$a-b...
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22 votes
3 answers
69
GATE CSE 1998 | Question: 1.2
Consider the following set of equations $x+2y=5$ $4x+8y=12$ $3x+6y+3z=15$ This set has unique solution has no solution has finite number of solutions has infinite number of solutions
Consider the following set of equations$x+2y=5$$4x+8y=12$$3x+6y+3z=15$This sethas unique solutionhas no solutionhas finite number of solutionshas infinite number of solut...
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20 votes
4 answers
70
GATE CSE 1998 | Question: 2.1
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$ $3$ $1$ $2$ $4$
The rank of the matrix given below is:$$\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$$$3$$1$$2$$4$
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5 votes
5 answers
71
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
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3 votes
2 answers
74
1. if V1 and V2 are eigenvectors that correspond to the distinct eigenvalues then they are linearly independent.
TRUE/FALSE :1. if V1 and V2 are eigenvectors that correspond to the distinct eigenvalues then they are linearly independent.2. if V1 and V2 are linearly independent eige...
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26 votes
7 answers
75
GATE CSE 2000 | Question: 1.3
The determinant of the matrix $\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}$ $4$ $0$ $15$ $20$
The determinant of the matrix $$\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}$$$4$$0$$15$$20$
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3 votes
2 answers
76
NIELIT 2016 MAR Scientist B - Section B: 12
If $A$ and $B$ are square matrices of size $n\times n$, then which of the following statements is not true? $\det(AB)=\det(A) \det(B)$ $\det(kA)=k^n \det(A)$ $\det(A+B)=\det(A)+\det(B)$ $\det(A^T)=1/\det(A^{-1})$
If $A$ and $B$ are square matrices of size $n\times n$, then which of the following statements is not true?$\det(AB)=\det(A) \det(B)$$\det(kA)=k^n \det(A)$$\det(A+B)=\det...
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21 votes
3 answers
78
GATE CSE 2005 | Question: 49
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$ $-1$ and $1$ $1$ and $6$ $2$ and $5$ $4$ and $-1$
What are the eigenvalues of the following $2\times 2$ matrix? $$\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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8 votes
4 answers
80
ISRO-DEC2017-1
Suppose $A$ is a finite set with $n$ elements.The number of elements and the rank of the largest equivalence relation on $A$ are $\{n,1\}$ $\{n,n\}$ $\{n^2,1\}$ $\{1,n^2\}$
Suppose $A$ is a finite set with $n$ elements.The number of elements and the rank of the largest equivalence relation on $A$ are$\{n,1\}$$\{n,n\}$$\{n^2,1\}$$\{1,n^2\}$
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