QQuestion
If A = \begin{bmatrix}2 & 2 \\ 0 & 2\end{bmatrix} and A² = \begin{bmatrix}4 & x \\ 0 & 4\end{bmatrix}, then the value of x is:
(a) 2
(b) 4
(c) 8
(d) 10
✓Answer
(c) 8
Explanation:
A² = A × A
A² = \begin{bmatrix}2 & 2 \\ 0 & 2\end{bmatrix}\begin{bmatrix}2 & 2 \\ 0 & 2\end{bmatrix}
= \begin{bmatrix}(2\times2)+(2\times0) & (2\times2)+(2\times2) \\ (0\times2)+(2\times0) & (0\times2)+(2\times2)\end{bmatrix}
= \begin{bmatrix}4 & 8 \\ 0 & 4\end{bmatrix}
Now, \begin{bmatrix}4 & 8 \\ 0 & 4\end{bmatrix} = \begin{bmatrix}4 & x \\ 0 & 4\end{bmatrix}
x = 8
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