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Question: If A = \(\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}\) and A<sup>–1</sup> = \(...

If A = [0121233a1]\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 value of a and c is -
A

1,1

B

1, – 1

C

1,2

D

– 1,1

Answer

1, – 1

Explanation

Solution

I = AA–1 = 12\frac{1}{2} [0121233a1]\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix} $\begin{bmatrix} 1 & - 1 & 1 \

  • 8 & 6 & 2c \ 5 & - 3 & 1 \end{bmatrix}$

= [10c+1012(c+1)4(1−a)3(a−1)2+ac]\begin{bmatrix} 1 & 0 & c + 1 \\ 0 & 1 & 2(c + 1) \\ 4(1 - a) & 3(a - 1) & 2 + ac \end{bmatrix}

comparing the elements of AA–1 with those of I,

c + 1 = 0 Ž c = –1

and a – 1 = 0 Ž a = 1