If A =[0010],\text{If A }= \begin{bmatrix}[r] 0 & 0 \ 1 & 0 \end{bmatrix},If A =[0100], then A2 =
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Given,
A=[0010]⇒A2=[0010][0010]=[0×0+0×10×0+0×01×0+0×11×0+0×0]=[0000] ∴A2=O.\text{A} = \begin{bmatrix}[r] 0 & 0 \ 1 & 0 \end{bmatrix} \\[1em] \Rightarrow \text{A}^2 = \begin{bmatrix}[r] 0 & 0 \ 1 & 0 \end{bmatrix}\begin{bmatrix}[r] 0 & 0 \ 1 & 0 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 0 \times 0 + 0 \times 1 & 0 \times 0 + 0 \times 0 \ 1 \times 0 + 0 \times 1 & 1 \times 0 + 0 \times 0 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 0 & 0 \ 0 & 0 \end{bmatrix} \\[1em]\ \therefore \text{A}^2 = O.A=[0100]⇒A2=[0100][0100]=[0×0+0×11×0+0×10×0+0×01×0+0×0]=[0000] ∴A2=O.
∴ Option 2 is the correct option.
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If x[23]+y[−10]=[106],x\begin{bmatrix}[r] 2 \ 3 \end{bmatrix} + y\begin{bmatrix}[r] -1 \ 0 \end{bmatrix} = \begin{bmatrix}[r] 10 \ 6 \end{bmatrix},x[23]+y[−10]=[106], then the values of x and y are
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 =[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
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]
