Question

If $5A=\left[\begin{array}{cc}3& -4\\ 4& x\end{array}\right]$ and $A{A}^T=A^{T}A=I$ then $x=?$

• A. $3$
• B. $-3$
• C. $2$
• D. $-2$

Answer 1

Answer: (A)

$3$

$5A^T=\left|\begin{array}{cc}3& 4\\ -4& x\end{array}\right|$

$25A^{T}A=\left|\begin{array}{cc}3& 4\\ -4& x\end{array}\right|\left|\begin{array}{cc}3& -4\\ 4& x\end{array}\right|$

$\left|\begin{array}{cc}25& 12-4x\\ 12-4x& 16+x^2\end{array}\right|$

Hence, we get

$12-4x=0$

$⟹x=3$