Register

GATE Mechanical 2014 Set 3 | Question: 1

• edited by
0 votes
0 votes

Consider a $3×3$ real symmetric matrix S such that two of its eigenvalues are $a\neq 0$, $b\neq 0$ with respective eigenvectors $\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$, $\begin{bmatrix} y_1\\ y_2\\ y_3 \end{bmatrix}$ If $a\neq b$ then $x_1y_1+x_2y_2+x_3y_3$ equals

  1. $a$
  2. $b$
  3. $ab$
  4. $0$
• edited by
User Avatar

Please log in or register to answer this question.

← PreviousNext →
← Previous in categoryNext in category →
Answer:

Related questions

0 answers
0 votes
Arjun asked Feb 19, 2017
GATE Mechanical 2014 Set 2 | Question: 1
One of the eigen vectors of the matrix $\begin{bmatrix} -5 & 2\\ -9 & 6 \end{bmatrix}$ is $\begin{Bmatrix} -1\\ 1 \end{Bmatrix} \\$ $\begin{Bmatrix} -2\\ 9 \end{Bmatrix} \\$ $\begin{Bmatrix} 2\\ -1 \end{Bmatrix} \\$ $\begin{Bmatrix} 1\\ 1 \end{Bmatrix} \\$
One of the eigen vectors of the matrix $\begin{bmatrix} -5 & 2\\ -9 & 6 \end{bmatrix}$ is$\begin{Bmatrix} -1\\ 1 \end{Bmatrix} \\$$\begin{Bmatrix} -2\\ 9 \end{Bmatrix} \\...
0 answers
0 votes
Arjun asked Feb 24, 2017
GATE2016-3-26
The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________
The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________
1 answers
0 votes
Arjun asked Feb 26, 2017
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 _________.
The determinant of a $2 \times 2$ matrix is $50$. If one eigenvalue of the matrix is $10$, the other eigenvalue is _________.
1 answers
0 votes
go_editor asked Mar 1, 2021
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: $\alpha$ $\alpha ^{2}$ $\surd{\alpha }$ $\alpha ^{4}$
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...
Voting & Accepting an answer helps improve the community
Link Copied!