Inverse of a 2 by 2 Matrix, and Solving with It Worksheet with Answer Key

What's on the worksheet

1. Find the inverse of each matrix, or show that it has none.
   \begin{bmatrix} 4 & 7 \\ 1 & 2 \end{bmatrix}\begin{bmatrix} -2 & 3 \\ 4 & -5 \end{bmatrix}\begin{bmatrix} 6 & -4 \\ -9 & 6 \end{bmatrix}\begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix}
2. Write the system as a matrix equation AX = B, find A^-1, and solve with X = A^-1B.
3. Let A = bmatrix x & x + 1 \\ x - 1 & x bmatrix, where x is any real number.
4. Let A = \begin{bmatrix} 5 & 2 \\ 2 & 1 \end{bmatrix} \qquad B = \begin{bmatrix} 4 & 1 \\ -2 & 0 \end{bmatrix} \qquad C = \begin{bmatrix} 9 & -3 \\ 0…
5. Four matrices are offered as the inverse of A = bmatrix 6 & 4 \\ 2 & 3 bmatrix:
6. A stall at a farmers' market sells honey at 7 dollars a jar and jam at 5 dollars a jar.