Question

Help? I don’t know the answer

Answer 1

`\left[ {\begin{array}{c} x_1 &\\x_2 \end{array} } \right] = \left[ {\begin{array}{cc} 0.5& - 3\\ 0 & 1 \\ \end{array} } \right] \left[ {\begin{array}{c} 2 &\\ - 3 \end{array} } \right]`

Step-by-step explanation

The given matrix is

`\left[ {\begin{array}{cc} 2 & 6\\ 0 & 1 \\ \end{array} } \right] \left[ {\begin{array}{c} x_1 &\\x_2 \end{array} } \right] = \left[ {\begin{array}{c} 2 &\\ - 3 \end{array} } \right]`

To solve this matrix, we need to multiply both sides of the matrix equation by the inverse of

`\left[ {\begin{array}{cc} 2 & 6\\ 0 & 1 \\ \end{array} } \right]`

The inverse of this matrix is

`(1)/(2 * 1 - 6 * 0) \left[ {\begin{array}{cc} 1 & - 6\\ 0 & 2 \\ \end{array} } \right] = \left[ {\begin{array}{cc} 0.5& - 3\\ 0 & 1 \\ \end{array} } \right]`

We multiply both sides by the inverse matrix to obtain;

`\left[ {\begin{array}{c} x_1 &\\x_2 \end{array} } \right] = \left[ {\begin{array}{cc} 0.5& - 3\\ 0 & 1 \\ \end{array} } \right] \left[ {\begin{array}{c} 2 &\\ - 3 \end{array} } \right]`

The correct choice is the last option.