search
Log In

Recent questions tagged eigen-value

1 vote
2 answers
1
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 447 views
2 votes
1 answer
3
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above
asked Feb 10, 2020 in Linear Algebra Lakshman Patel RJIT 335 views
5 votes
3 answers
4
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
asked Sep 23, 2019 in Linear Algebra Arjun 400 views
1 vote
2 answers
5
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix $A \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & – \sin t & \cos t \end{pmatrix}.$ If $\lambda_1+\lambda_2+\lambda_3 = \sqrt{2}+1$, then the set of possible values of $t, \: – \pi \leq t < \pi$, is Empty set $\{ \frac{\pi}{4} \}$ $\{ – \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{ – \frac{\pi}{3}, \frac{\pi}{3} \}$
asked Sep 23, 2019 in Linear Algebra Arjun 332 views
1 vote
1 answer
6
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$
asked Sep 23, 2019 in Linear Algebra Arjun 277 views
0 votes
0 answers
7
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
asked May 28, 2019 in Linear Algebra Hirak 167 views
0 votes
1 answer
8
Let $A$ be a $3Γ— 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $-4$ $-2$ $2$ $4$
asked May 11, 2019 in Linear Algebra akash.dinkar12 617 views
0 votes
0 answers
9
2 votes
1 answer
10
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $-a,2a,2a$ $a,a+\sqrt{2},a-\sqrt{2}$
asked Apr 25, 2019 in Linear Algebra Hirak 282 views
13 votes
4 answers
11
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
asked Feb 7, 2019 in Linear Algebra Arjun 8.6k views
0 votes
0 answers
12
asked Jan 31, 2019 in Linear Algebra Hemanth_13 153 views
0 votes
2 answers
13
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=? a)24 b)-2 c)12 d)-12 Please explain in detail.
asked Jan 19, 2019 in Linear Algebra Reshu $ingh 1.3k views
0 votes
0 answers
14
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?
asked Jan 4, 2019 in Linear Algebra Shamim Ahmed 207 views
7 votes
2 answers
16
$A$ is $n \times n$ square matrix for which the entries in every row sum to $1$. Consider the following statements: The column vector $[1,1,\ldots,1]^T$ is an eigen vector of $A.$ $ \text{det}(A-I) = 0.$ $\text{det}(A) = 0.$ Which of the above statements must be TRUE? Only $(i)$ Only $(ii)$ Only $(i)$ and $(ii)$ Only $(i)$ and $(iii)$ $(i),(ii) \text{ and }(iii)$
asked Dec 18, 2018 in Linear Algebra Arjun 1.5k views
1 vote
1 answer
17
Eigenvalues of an Idempotentmatrix matrix A is 0 or 1 right or wrong?
asked Dec 15, 2018 in Linear Algebra sahadeo2494 127 views
1 vote
1 answer
18
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigen vector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is $15$ $16$ $17$ $18$
asked Dec 7, 2018 in Linear Algebra Arjun 550 views
0 votes
0 answers
21
If $A$ is $2\times 2$ matrix ,eigen value is $1,-2$ and corresponding eigen vector $[1,2]^{T}$ and $[9,1]^{T}$.find sum of element of the matrix $A.$
asked Nov 15, 2018 in Linear Algebra amit166 134 views
1 vote
1 answer
22
0 votes
0 answers
23
0 votes
0 answers
24
Given that a matrix $A_{3\times3},$which is not idempotent matrix.And $A^{3}=A.$ Then find them, $1)$ Eigen Values $2)$ Trace of the matrix$=$Sum of Leading Diagonal Elements$=\sum a_{ij},$ where $i=j$ $3)Det(A)$
asked Oct 25, 2018 in Linear Algebra Lakshman Patel RJIT 181 views
0 votes
0 answers
25
Given that the matrix $A=\begin{bmatrix} a_{11} &a_{12} \\ a_{21} &a_{22} \end{bmatrix}$ and Eigen value are $1,-2$ and Corresponding Eigen Vectors are $X_{1}=\begin{bmatrix} 1\\2 \end{bmatrix}$ and $X_{2}=\begin{bmatrix} 9\\1 \end{bmatrix}$ Find the $1)\sum a_{ij},$when $i=j$ $2)Det(A)$ $3)$Sum of all Elements in the given matrix
asked Oct 25, 2018 in Linear Algebra Lakshman Patel RJIT 217 views
...