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Syllabus: Matrices, determinants, System of linear equations, Eigenvalues and eigenvectors, LU decomposition.

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&1&1&1&1&1&2&1&1.2&2
\\\hline\textbf{2 Marks Count}&1&1&2&1&0&0&0&0.8&2
\\\hline\textbf{Total Marks}&3&3&5&3&1&2&\bf{1}&\bf{2.5}&\bf{5}\\\hline
\end{array}}}$$

Recent questions in Linear Algebra

4 votes
3 answers
1
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
asked Feb 18 in Linear Algebra Arjun 592 views
1 vote
2 answers
2
For a statement $S$ in a program, in the context of liveness analysis, the following sets are defined: $\text{USE(S)}$ : the set of variables used in $S$ $\text{IN(S)}$ : the set of variables that are live at the entry of $S$ $\text{OUT(S)}$ : the set of variables that are live at the exit ... $) }\cup \text{ OUT ($S_2$)}$ $\text{OUT ($S_1$)}$ = $\text{USE ($S_1$)} \cup \text{IN ($S_2$)}$
asked Feb 18 in Linear Algebra Arjun 316 views
1 vote
2 answers
3
Consider the following matrix. $\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$ The largest eigenvalue of the above matrix is __________.
asked Feb 18 in Linear Algebra Arjun 469 views
1 vote
1 answer
4
Consider the matrix $A=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Find $A^n,$ in terms of $n,$ for $n\geq2.$
asked Jan 29 in Linear Algebra soujanyareddy13 76 views
0 votes
2 answers
5
The matrices $\begin{bmatrix} \cos\theta &-\sin \theta \\ \sin \theta & cos \theta \end{bmatrix}$ and $\begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix}$ commute under the multiplication if $a=b \text{(or)} \theta =n\pi, \: n$ is an integer always never if $a\cos \theta \neq b\sin \theta$
asked Apr 2, 2020 in Linear Algebra Lakshman Patel RJIT 171 views
0 votes
1 answer
6
0 votes
1 answer
7
Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is true $x$ and $y$ are linearly independent $x$ and $y$ are linearly dependent $x$ and $z$ are linearly dependent $y$ and $z$ are linearly dependent
asked Apr 2, 2020 in Linear Algebra Lakshman Patel RJIT 114 views
0 votes
0 answers
8
If product of matrix $A=\begin{bmatrix}\cos^{2}\theta &\cos \theta \sin \theta \\ \cos \theta \sin \theta &\sin ^{2} \theta& \end{bmatrix}$ and $B=\begin{bmatrix}\cos^{2}\phi &\cos \phi \sin \phi \\ \cos \phi \sin \phi &\sin ^{2} \phi& \end{bmatrix}$ is a ... and $\phi$ differ by an odd multiple of $\pi$ even multiple of $\pi$ odd multiple of $\dfrac{\pi}{2}$ even multiple of $\dfrac{\pi}{2}$
asked Apr 2, 2020 in Linear Algebra Lakshman Patel RJIT 123 views
0 votes
1 answer
9
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiplied by $2,$ its determinant value becomes $40.$ The value of $’n’$ is $2$ $3$ $5$ $4$
asked Apr 1, 2020 in Linear Algebra Lakshman Patel RJIT 166 views
0 votes
2 answers
10
0 votes
1 answer
11
0 votes
1 answer
12
0 votes
2 answers
13
If $A$ and $B$ are square matrices of size $n\times n$, then which of the following statements is not true? $\det(AB)=\det(A) \det(B)$ $\det(kA)=k^n \det(A)$ $\det(A+B)=\det(A)+\det(B)$ $\det(A^T)=1/\det(A^{-1})$
asked Mar 31, 2020 in Linear Algebra Lakshman Patel RJIT 945 views
1 vote
2 answers
15
0 votes
1 answer
16
Consider two matrices $M_1$ and $M_2$ with $M_1^*M_2=0$ and $M_1$ is non singular. Then which of the following is true? $M_2$ is non singular $M_2$ is null matrix $M_2$ is the identity matrix $M_2$ is transpose of $M_1$
asked Mar 30, 2020 in Linear Algebra Lakshman Patel RJIT 201 views
1 vote
2 answers
17
$AVA=A$ is called : Identity law De Morgan’s law Idempotent law Complement law
asked Mar 26, 2020 in Linear Algebra jothee 117 views
0 votes
0 answers
18
How many corner does a cube have in 4 dimensions? How many 3D faces? Now by observation we can tell that, an n-dimensional cube has $2^n$ corners. 1D cube which is a line have $2^1$ corners 2D cube which is a square have $2^2$ corners 3D cube have $2^3$ corners ... 8 three-dimension cubes. but this is the question i'm not able to answer. How every N-cube have $|2n|$ cubes of dimension (N-1)?
asked Feb 26, 2020 in Linear Algebra Mk Utkarsh 257 views
8 votes
5 answers
19
Let $G$ be a group of $35$ elements. Then the largest possible size of a subgroup of $G$ other than $G$ itself is _______.
asked Feb 12, 2020 in Linear Algebra Arjun 3.5k views
5 votes
3 answers
20
Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider the following statements. $\text{rank}(AB) = \text{rank }(A) \text{rank }(B)$ ... Which of the above statements are TRUE? I and II only I and IV only II and III only III and IV only
asked Feb 12, 2020 in Linear Algebra Arjun 3.2k views
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