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Recent questions and answers in Linear Algebra

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GATE Mechanical 2021 Set 2 | Question: 1
Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $p.$ Their product $Ap=\alpha ^{2}p$, where $\alpha \in \Re$ and $\alpha \notin \left \{ -1,0,1 \right \}$. Based on the given information, the eigen value of $A^{2}$ is: $\alpha$ $\alpha ^{2}$ $\surd{\alpha }$ $\alpha ^{4}$
ShouvikSVK answered in Linear Algebra Jan 22, 2022
by ShouvikSVK
280 points
1 answer
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GATE2020-ME-2: 2
A matrix $P$ is decomposed into its symmetric part $S$ and skew symmetric part $V$ ... $\begin{pmatrix} -2 & 9/2 & -1 \\ -1 & 81/4 & 11 \\ -2 & 45/2 & 73/4 \end{pmatrix}$
haralk10 answered in Linear Algebra Dec 2, 2020
by haralk10
180 points
1 answer
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GATE2017 ME-2: 28
Consider the matrix $A=\begin{bmatrix} 50 &70 \\ 70 & 80 \end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda _{1}$ and $\lambda _{2}$ are $x_{1}=\begin{bmatrix} 70 \\ \lambda_{1}-50 \end{bmatrix}$ and $x_{2}=\begin{bmatrix} \lambda _{2}-80\\ 70 \end{bmatrix}$, respectively. The value of $x^{T}_{1} x_{2}$ is _________.
ankitgupta.1729 answered in Linear Algebra May 24, 2019
by ankitgupta.1729
410 points
1 answer
0 votes
GATE2019 ME-2: 1
In matrix equation $[A] \{X\}=\{R\}$, $[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{ and} \{ R \} = \begin{Bmatrix} 32 \\ 16 \\ 64 \end{Bmatrix}$ One of the eigen values of matrix $[A]$ is $4$ $8$ $15$ $16$
ankitgupta.1729 answered in Linear Algebra May 24, 2019
by ankitgupta.1729
410 points
1 answer
1 vote
GATE2019 ME-1: 1
Consider the matrix $P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ The number of distinct eigenvalues $0$ $1$ $2$ $3$
aditya_kr answered in Linear Algebra Feb 15, 2019
by aditya_kr
160 points
1 answer
0 votes
GATE2018-2-19
If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{-1})$ is _______ (correct to two decimal palces).
Balaji Jegan answered in Linear Algebra Feb 22, 2018
by Balaji Jegan
1.2k points
1 answer
0 votes
GATE2017 ME-2: 3
The determinant of a $2 \times 2$ matrix is $50$. If one eigenvalue of the matrix is $10$, the other eigenvalue is _________.
m2n037 answered in Linear Algebra Feb 14, 2018
by m2n037
940 points
1 answer
0 votes
GATE Mechanical 2014 Set 4 | Question: 1
Which one of the following equations is a correct identity for arbitrary $3 \times 3$ real matrices $P$, $Q$ and $R$? $P(Q+R)=PQ+RP$ $(P-Q)^2 = P^2 -2PQ -Q^2$ $\text{det } (P+Q)= \text{det } P+ \text{det } Q$ $(P+Q)^2=P^2+PQ+QP+Q^2$
annie1234 answered in Linear Algebra Apr 6, 2017
by annie1234
460 points
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