CPM Homework Help : PC Problem 12-9

Let and . Homework Help ✎
1. Find MN.
2. Find values for a, b, c, and d so that MN = I.
3. Use the results of (b) to find M⁻¹.

Step (a):

$\begin{bmatrix}1(a)+0(c)&1(b)+0(d)\\-1(a)+2(c)&-1(b)+2(d)\end{bmatrix}$

Hint (b):

$I=\begin{bmatrix}1&0\\0&1\end{bmatrix}$

Step (b):

Using the lower left entry from part (a) and matrix I:
−1(a) + 2(c) = 0
Now repeat this process for the rest of the entries.

Hint (c):

Look at part (b) and remember that M(M⁻¹) = I.