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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

0 votes
1 answer
151
Rank
IF A is square matrix of order 'n' and rank(A)=n-2 then Rank(adj(A))=?
IF A is square matrix of order 'n' and rank(A)=n-2 then Rank(adj(A))=?
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1 votes
1 answer
152
made easy ME previou year question
which on of the following is an eigenvector of the matrix [5 0 0 0 0 5 5 0 0 0 2 1 0 0 3 1] a) [1 -2 0 0 ]t b) [0 0 1 0]t c) [1 0 0 -2]t d) [1 -1 2 1]t
which on of the following is an eigenvector of the matrix[5 0 0 0 0 5 5 0 0 0 2 1 0 0 3 1]a) [1 -2 0 0 ]tb) [0 0 1 0]tc) [1 0 0 -2]td) [1 -1 2 1]t
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0 votes
1 answer
154
Consider the series Xn+1 = Xn / 2 + 98 Xn, X0 = 0.5 obtained from the Newton-Raphson method. The series converges to
Can any1 solve this plsoptions:A)1.5 B)sqrt(2)C)1.6D)1.4
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8 votes
2 answers
155
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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10 votes
8 answers
156
ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$
Suppose the rank of the matrix$$\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$$is $2$ for some real numbers $a$ and $b$. Then $b$ equals$1$$3$$1/2$$1/3$
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6 votes
3 answers
158
ISRO-DEC2017-17
If $C$ is a skew-symmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is a scalar matrix null matrix unit matrix matrix will all elements $1$
If $C$ is a skew-symmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is ascalar matrixnull matrixunit matrixmatrix will all elements $1$
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2 votes
1 answer
159
EE,2016
Consider a $3\times 3$ matrix with every element being equal to 1 , its only non-zero eigenvalue is ....? $3\times 3 \begin{bmatrix} 1 & 1 &1 \\ 1 &1 &1 \\ 1 &1 &1 \end{bmatrix}$ ... but i got different eigen values why this happened ... i missed something ??
Consider a $3\times 3$ matrix with every element being equal to 1 , its only non-zero eigenvalue is ....?$3\times 3 \begin{bmatrix} 1 & 1 &1 \\ 1 &1 &1 \\ 1 &1 &1 \end{bm...
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0 votes
1 answer
160
Gate 2015 CE set 2
The two eigen values of the matrix $\begin{bmatrix} 2 & 1\\ 1& p \end{bmatrix}$ have a ratio of 3:1 for p= 2. What is another value of p for which eigenvalues have the same ratio of 3:1? A)-2 b) 1 c) 7/3 d)14/3
The two eigen values of the matrix $\begin{bmatrix} 2 & 1\\ 1& p \end{bmatrix}$ have a ratio of 3:1 for p= 2.What is another value of p for which eigenvalues have the sam...
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1 votes
1 answer
161
Characteristic Equation of MAtrix
Conventional way to find the characteristic equation is tough here...Any efficient way anyone?
Conventional way to find the characteristic equation is tough here...Any efficient way anyone?
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0 votes
1 answer
163
characteristics polynomial
A is 5×5 matrix, all of whose entries are 1, then (a) A is not diagonalizable (b) A is idempotent (c) A is nilpotent (d) The minimal polynomial and the characteristics polynomial of A are not equal
A is 5×5 matrix, all of whose entries are 1, then(a) A is not diagonalizable(b) A is idempotent(c) A is nilpotent(d) The minimal polynomial and the characteristics polyn...
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0 votes
1 answer
164
ISRO 2013 - matrices [Mech]
If A=$\begin{bmatrix} 8 & 5 & \\ 7& 6 & \end{bmatrix}$ then |$A^{121}$ - $A^{120}$ | is: a) 0 b) 1 c) 120 d) 121
If A=$\begin{bmatrix} 8 & 5 & \\ 7& 6 & \end{bmatrix}$ then |$A^{121}$ - $A^{120}$ | is:a) 0b) 1c) 120d) 121
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2 votes
1 answer
165
Gate 2014
Qus 1 Qus2
Qus 1Qus2
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1 votes
1 answer
167
Made easy workbook
Let $A = (a_{ij})_{n\times n}$ such that $a_{ij}=3$ for all $i,j$ then nullity of $A$ is $n-1$ $n-3$ $n$ $0$
Let $A = (a_{ij})_{n\times n}$ such that $a_{ij}=3$ for all $i,j$ then nullity of $A$ is$n-1$$n-3$$n$$0$
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3 votes
4 answers
168
GATE2017 EC
The rank of the matrix $\begin{bmatrix} 1 & -1 & 0 &0 & 0\\ 0 & 0 & 1 &-1 &0 \\ 0 &1 &-1 &0 &0 \\ -1 & 0 &0 & 0 &1 \\ 0&0 & 0 & 1 & -1 \end{bmatrix}$ is ________. Ans 5?
The rank of the matrix$\begin{bmatrix} 1 & -1 & 0 &0 & 0\\ 0 & 0 & 1 &-1 &0 \\ 0 &1 &-1 &0 &0 \\ -1 & 0 &0 & 0 &1 \\ 0&0 & 0 & 1 & -1 \end{bmatrix}$is ________.Ans 5?
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3 votes
1 answer
169
GATE_2014 ME
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a ≠ b then x1y1 + x2y2 + x3y3 is a) a b) b c) ab d) 0
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a &ne...
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1 votes
1 answer
170
ugcnet_june_2008_II
5. In a set of 8 positive integers, there always exists a pair of numbers having the same remainder when divided by: .(A) 7 (B) 11 (C) 13 (D) 15
5. In a set of 8 positive integers, there always exists a pair of numbers having the same remainder when divided by:.(A) 7 (B) 11 (C) 13 ...
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