If A = begin{bmatrix} 0 & 1 0 & 0 end{bmatri | vedclass

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

Question

(B) Given $A = \begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$.First,calculate $aI + bA$:$aI + bA

Vedclass · Accepted Answer

$a^2I + 2abA$

Vedclass · Answer

(B) Given $A = \begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$.First,calculate $aI + bA$:$aI + bA = a \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} + b \begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix} = \begin{bmatrix} a & 0 \ 0 & a \end{bmatrix} + \begin{bmatrix} 0 & b \ 0 & 0 \end{bmatrix} = \begin{bmatrix} a & b \ 0 & a \end{bmatrix}$.Now,calculate $(aI + bA)^2$:$(aI + bA)^2 = \begin{bmatrix} a & b \ 0 & a \end{bmatrix} \begin{bmatrix} a & b \ 0 & a \end{bmatrix} = \begin{bmatrix} a^2 + 0 & ab + ba \ 0 + 0 & 0 + a^2 \end{bmatrix} = \begin{bmatrix} a^2 & 2ab \ 0 & a^2 \end{bmatrix}$.This can be written as:$a^2 \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} + 2ab \begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix} = a^2I + 2abA$.

If $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$,$I$ is the identity matrix of order $2$,and $a, b$ are arbitrary constants,then $(aI + bA)^2$ is equal to

Similar Questions

Let $A = \begin{bmatrix} b^2+c^2 & a^2 & a^2 \\ b^2 & c^2+a^2 & b^2 \\ c^2 & c^2 & a^2+b^2 \end{bmatrix}$. If $a = \sin \frac{\pi}{6}$,$b = \cos \frac{\pi}{4}$,and $c = \cot \frac{\pi}{2}$,then $A$ is:

If $A$ is a square matrix for which $a_{ij} = i^2 - j^2$,then $A$ is

If $A_1, A_3, \dots, A_{2n-1}$ are $n$ skew-symmetric matrices of the same order,then $B = \sum_{r=1}^n (2r-1)(A_{2r-1})^{2r-1}$ will be:

The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:

If the matrix $\begin{bmatrix} x & x^2+3x & 5 \\ -2x-6 & x^2 & -4x-2 \\ 5 & x^2+2 & x^3 \end{bmatrix}$ is a symmetric matrix, then the value of $x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module