Question

In matrix equation [A] {X} = {R},

[A] = $\left[\begin{array}{ccc}4& 8& 4\\ 8& 16& -4\\ 4& -4& 15\end{array}\right]$, $\left\{X\right\}=\left\{\begin{array}{c}2\\ 1\\ 4\end{array}\right\}$ and $\left\{R\right\}=\left\{\begin{array}{c}32\\ 16\\ 64\end{array}\right\}$

One of the eigen values of matrix [A] is

• A. 16
• B. 8
• C. 15
• D. 4

Answer 1

The correct option is A 16

In matrix equation A[X] = {R}

A[X] can also be substituted by $\lambda \left[X\right]$

Choosing from option '16' first

16[X] = 16$\left\{\begin{array}{c}2\\ 1\\ 4\end{array}\right\}$ = $\left\{\begin{array}{c}32\\ 16\\ 64\end{array}\right\}$

As 16 satisfies the equation, the correct option is (a).