Recent questions tagged eigen-value

3 votes
2 answers
181
The number of linearly independent Eigen vectors of is a) 0b) 1 C) 2d) infinite
3 votes
1 answer
182
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...
4 votes
3 answers
184
In A = (aij)nxn where aij = 1 ∀ i,j then number of different independent Eigen Vectors of A are _________ . (a) 1(b) n-1(c) 2(d) n
3 votes
1 answer
185
The possible set of eigen values of a $4*4$ skew symmetric; orthogonal real matrix is A). $\pm i$B), $(\pm i,\pm1)$C). $\pm1$D). $(0,\pm i)$
4 votes
3 answers
188
Eigenvalue of matrix $A$ , $\begin{bmatrix} 2 &7 &10 \\ 5& 2 & 25\\ 1& 6 &5 \end{bmatrix}$ is $-9.33$ other eigenvalue is1) $18.3...
4 votes
1 answer
190
Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ hasAn eigenvalue which is purely imaginaryAt least one real eigenvalueAt least two eigenvalues which are not ...
3 votes
2 answers
191
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...
23 votes
3 answers
195
25 votes
8 answers
196
What are the eigenvalues of the matrix $P$ given below$$P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$$ $a, a -√2, a + √2...
61 votes
8 answers
197
25 votes
5 answers
198
97 votes
8 answers
200
The product of the non-zero eigenvalues of the matrix is ____$\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & ...
60 votes
4 answers
201
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________
21 votes
3 answers
202
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$$4$ and $-1$...
22 votes
4 answers
203
Consider the following matrix $$A = \left[\begin{array}{cc}2 & 3\\x & y \end{array}\right]$$ If the eigenvalues of A are $4$ and $8$, then$x = 4$, $y = 10$$x = 5$, $y = 8...
28 votes
5 answers
204
Obtain the eigen values of the matrix$$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & -2 & 104 \\ 0 & 0 & 0 & -1 \end{bmatrix}$$
49 votes
7 answers
205
The eigen vector $(s)$ of the matrix $$\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$$ is (are)$(0,0,\alpha)$$(\alpha,0,0)$$(0,0,1)$$(0,\al...
79 votes
5 answers
207
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $...