Question

if $\begin{bmatrix}a+b&2\\ 5&ab\end{bmatrix} = \begin{bmatrix}6&2\\ 5&8\end{bmatrix}$, then find the values of a and b respectively

• A. $ 2,4 $
• B. $ 4,2 $
• C. Both (a) & (b)
• D. None of these

Answer 1

Answer: (C)

since $\begin{bmatrix}a+b&2\\ 5&ab\end{bmatrix} = \begin{bmatrix}6&2\\ 5&8\end{bmatrix}$
$\Rightarrow a+ b = 6$ and $ab = 8$
$\Rightarrow a+\frac{ 8}{a } = 6 \,\,\,\,\, (\therefore ab = 8 \Rightarrow b =\frac{8 }{ a})$
$\Rightarrow a^{2} - 6a + 8 = 0 $
$\Rightarrow (a - 2) (a - 4) = 0$
$\Rightarrow a =2,4$
hence, $a=2, b = 4$, or $a = 4 , b=2$