Let A = begin{bmatrix} 3 & 0 & 3 0 & 3 & 0 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the matrix $A = \begin{bmatrix} 3 & 0 & 3 \ 0 & 3 & 0 \ 3 & 0 & 3 \end{bmatrix}$.The characteristic equation is given by $\operatorname{de

Vedclass · Accepted Answer

$0, 3, 6$

Vedclass · Answer

(B) Given the matrix $A = \begin{bmatrix} 3 & 0 & 3 \ 0 & 3 & 0 \ 3 & 0 & 3 \end{bmatrix}$.The characteristic equation is given by $\operatorname{det}(A - \lambda I_{3}) = 0$.$\begin{vmatrix} 3-\lambda & 0 & 3 \ 0 & 3-\lambda & 0 \ 3 & 0 & 3-\lambda \end{vmatrix} = 0$.Expanding along the second row:$(3-\lambda) \begin{vmatrix} 3-\lambda & 3 \ 3 & 3-\lambda \end{vmatrix} = 0$.$(3-\lambda) [(3-\lambda)^2 - 9] = 0$.$(3-\lambda) [9 + \lambda^2 - 6\lambda - 9] = 0$.$(3-\lambda) (\lambda^2 - 6\lambda) = 0$.$(3-\lambda) \lambda (\lambda - 6) = 0$.Thus, the roots are $\lambda = 0, 3, 6$.

Let $A = \begin{bmatrix} 3 & 0 & 3 \\ 0 & 3 & 0 \\ 3 & 0 & 3 \end{bmatrix}$. Then, the roots of the equation $\operatorname{det}(A - \lambda I_{3}) = 0$ (where $I_{3}$ is the identity matrix of order $3$) are

Similar Questions

Let $P=\begin{bmatrix} 1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1 \end{bmatrix}$ and $I$ be the identity matrix of order $3$. If $Q=[q_{ij}]$ is a matrix such that $P^{50}-Q=I$,then $\frac{q_{31}+q_{32}}{q_{21}}$ equals

If $A$ and $B$ are square matrices of order $3$,then $|(A-A^T)+(B-B^T)|=$

If $A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then which one of the following statements is not correct?

The total number of $3 \times 3$ matrices $A$ having entries from the set $\{0, 1, 2, 3\}$ such that the sum of all the diagonal entries of $AA^{T}$ is $9$,is equal to........

If $A = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ and $M = A + A^{2} + A^{3} + \dots + A^{20}$,then the sum of all the elements of the matrix $M$ is equal to $.....$

Vedclass Test Series

Exam Paper Generator

Online Exam Module