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

If A = [0121233x1]\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1 \end{bmatrix}and A–1= $\begin{bmatrix} 1/2 & - 1/2 & 1/2 \

  • 4 & 3 & y \ 5/2 & - 3/2 & 1/2 \end{bmatrix}$, then -
A

x = 1, y = –1

B

x = –1, y = 1

C

x = 2, y = –1/2

D

x = 1/2, y = ½

Answer

x = 1, y = –1

Explanation

Solution

We have

[100010001]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}= AA–1 = [0121233x1]\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1 \end{bmatrix}

1/2 & - 1/2 & 1/2 \\ - 4 & 3 & y \\ 5/2 & - 3/2 & 1/2 \end{bmatrix}$$ = $\begin{bmatrix} 1 & 0 & y + 1 \\ 0 & 1 & 2(y + 1) \\ 4(1 - x) & 3(x - 1) & 2 + xy \end{bmatrix}$ 1 – x = 0, x – 1 = 0, y + 1 = 0, y + 1 = 0, 2 + xy = 1 x = 1, y = –1.