If A =[1011],\text{If A }= \begin{bmatrix}[r] 1 & 0 \ 1 & 1 \end{bmatrix},If A =[1101], then A2 =
[2011]\begin{bmatrix}[r] 2 & 0 \ 1 & 1 \end{bmatrix}[2101]
[1012]\begin{bmatrix}[r] 1 & 0 \ 1 & 2 \end{bmatrix}[1102]
[1021]\begin{bmatrix}[r] 1 & 0 \ 2 & 1 \end{bmatrix}[1201]
none of these
4 Likes
Given,
A=[1011]⇒A2=[1011][1011]=[1×1+0×11×0+0×11×1+1×11×0+1×1]=[1021] ∴A2=[1021].\text{A} = \begin{bmatrix}[r] 1 & 0 \ 1 & 1 \end{bmatrix} \\[0.5em] \Rightarrow \text{A}^2 = \begin{bmatrix}[r] 1 & 0 \ 1 & 1 \end{bmatrix}\begin{bmatrix}[r] 1 & 0 \ 1 & 1 \end{bmatrix} \\[0.5em] = \begin{bmatrix}[r] 1 \times 1 + 0 \times 1 & 1 \times 0 + 0 \times 1 \ 1 \times 1 + 1 \times 1 & 1 \times 0 + 1 \times 1 \end{bmatrix} \\[0.5em] = \begin{bmatrix}[r] 1 & 0 \ 2 & 1 \end{bmatrix} \\[0.5em]\ \therefore \text{A}^2 = \begin{bmatrix}[r] 1 & 0 \ 2 & 1 \end{bmatrix}.A=[1101]⇒A2=[1101][1101]=[1×1+0×11×1+1×11×0+0×11×0+1×1]=[1201] ∴A2=[1201].
∴ Option 3 is the correct option.
Answered By
2 Likes
If A =[0110],\text{If A }= \begin{bmatrix}[r] 0 & 1 \ 1 & 0 \end{bmatrix},If A =[0110], then A2 =
[1100]\begin{bmatrix}[r] 1 & 1 \ 0 & 0 \end{bmatrix}[1010]
[0011]\begin{bmatrix}[r] 0 & 0 \ 1 & 1 \end{bmatrix}[0101]
[0110]\begin{bmatrix}[r] 0 & 1 \ 1 & 0 \end{bmatrix}[0110]
[1001]\begin{bmatrix}[r] 1 & 0 \ 0 & 1 \end{bmatrix}[1001]
If A =[0010],\text{If A }= \begin{bmatrix}[r] 0 & 0 \ 1 & 0 \end{bmatrix},If A =[0100], then A2 =
If A =[31−12],\text{If A }= \begin{bmatrix}[r] 3 & 1 \ -1 & 2 \end{bmatrix},If A =[3−112], then A2 =
[85−53]\begin{bmatrix}[r] 8 & 5 \ -5 & 3 \end{bmatrix}[8−553]
[8−553]\begin{bmatrix}[r] 8 & -5 \ 5 & 3 \end{bmatrix}[85−53]
[8−5−5−3]\begin{bmatrix}[r] 8 & -5 \ -5 & -3 \end{bmatrix}[8−5−5−3]
[8−5−53]\begin{bmatrix}[r] 8 & -5 \ -5 & 3 \end{bmatrix}[8−5−53]
If matrix 𝐴 = [2202] and A2=[4x04]\begin{bmatrix}[r] 2 & 2 \ 0 & 2 \end{bmatrix}\text{ and } A^2 = \begin{bmatrix}[r] 4 & x \ 0 & 4 \end{bmatrix}[2022] and A2=[40x4], then the value of x is :
2
4
8
10
