MCQ
If $A =\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right], B =\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right]$ and $A ^2= B$, then the value of $x$ is :
- A26
- B30
- ✓36
- D40
✓
Answer
Correct option: C.
36
(c) 36
Explanation :
$\begin{array}{l}A^2=B \\ \Rightarrow A \cdot A \cdot=B \\ \Rightarrow\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right] \\ \Rightarrow\left[\begin{array}{cc}4 & 36 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right] \\ \Rightarrow x=36\end{array}$
Explanation :
$\begin{array}{l}A^2=B \\ \Rightarrow A \cdot A \cdot=B \\ \Rightarrow\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right] \\ \Rightarrow\left[\begin{array}{cc}4 & 36 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right] \\ \Rightarrow x=36\end{array}$
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