Question

Let X= $\begin{bmatrix} x \\ y \\ z \end{bmatrix}$, D = $\begin{bmatrix} 3 \\ 5 \\ 11 \end{bmatrix}$and A = $\begin{bmatrix} 1 & - 1 & - 2 \\ 2 & 1 & 1 \\ 4 & - 1 & - 2 \end{bmatrix}$. If X = A^–1 D, then X is equal to

• A. $\begin{bmatrix} 1 \\ 0 \\ 2 \end{bmatrix}$
• B. $\begin{bmatrix} 8/3 \
  • 1/3 \ 0 \end{bmatrix}$
• C. $\begin{bmatrix}
  • 8/3 \ 1 \ 0 \end{bmatrix}$
• D. $\begin{bmatrix} 8/3 \ 1/3 \
  • 1 \end{bmatrix}$

Answer 1

Answer: (B)

$\begin{bmatrix} 8/3 \

• 1/3 \ 0 \end{bmatrix}$

Answer 2

Since A = $\begin{bmatrix} 1 & - 1 & - 2 \\ 2 & 1 & 1 \\ 4 & - 1 & - 2 \end{bmatrix}$

\ A^–1 =$\frac { 1 } { 3 }$ $\begin{bmatrix}

• 1 & 0 & 1 \ 8 & 6 & - 5 \
• 6 & - 3 & 3 \end{bmatrix}$

A^–1 D = $\frac { 1 } { 3 }$ $\begin{bmatrix} 8 \

• 1 \ 0 \end{bmatrix}$

Ž $\begin{bmatrix} x \\ y \\ z \end{bmatrix}$= $\begin{bmatrix} 8/3 \

• 1/3 \ 0 \end{bmatrix}$