Question

If A = $\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}$ and A^–1 = $\begin{bmatrix} 1/2 & –1/2 & 1/2 \\ –4 & 3 & c \\ 5/2 & –3/2 & 1/2 \end{bmatrix}$, then the value of a and c is equal to –

• A. –1, 1
• B. 1, 2
• C. 1, – 1
• D. 1, 1

Answer 1

Answer: (C)

1, – 1

Answer 2

AA^–1 = I

$\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}$ $\overset{\downarrow \downarrow}{\begin{bmatrix} 1/2 & –1/2 & 1/2 \\ –4 & 3 & c \\ 5/2 & –3/2 & –1/2 \end{bmatrix}}$ = $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

Comparing (a₃₁)

Ž $\frac{3}{2}$ – 4a + $\frac{5}{2}$ = 0

4 – 4a = 0

a = 1 \end{matrix}$$ Comparing (a₁₃) 0 + C + 1 0 C = – 1