Question

30 Points!!

Answer 1

Answer:

  multiply the left side of the constant vector by the inverse matrix

Step-by-step explanation:

The matrix equation ...

  AX = B

is solved by left-multiplying by the inverse of A:

  A⁻¹AX = A⁻¹B

  IX = A⁻¹B . . . . . the result of multiplying A⁻¹A is the identity matrix

  X = A⁻¹B . . . . . B needs to be multiplied by the inverse matrix

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}-4&1\\3&2\end{array}\right]^{-1}\left[\begin{array}{c}9&7\end{array}\right]=\dfrac{1}{11}\left[\begin{array}{cc}-2&1\\3&4\end{array}\right]\left[\begin{array}{c}9&7\end{array}\right]=\left[\begin{array}{c}-1&5\end{array}\right]$