Question

Solve for the matrix a in terms of the others in the following equation: p -1(d ca)p = b if you need to use an inverse, assume it exists?

Answer 1

To solve for matrix a in the equation p^-1(d ca)p = b, we need to isolate a. The solution is a = (d^-1)(c^-1).

Step-by-step explanation:

To solve for matrix a in the equation p-1(d ca)p = b, we need to isolate a. Here are the steps:

1. Apply the inverse of p to both sides of the equation: p-1(d ca)p(p-1) = b(p-1).
2. Simplify by cancelling out the p-1 and p terms: d ca = b(p-1).
3. Apply the inverse of b(p-1) to both sides: (d ca)(b(p-1))-1 = (b(p-1))(b(p-1))-1.
4. Simplify using matrix multiplication and the fact that (X-1)-1 = X: ac = (d-1).
5. Finally, isolate a: a = (d-1)(c-1).

Therefore, the solution for matrix a in terms of the others is a = (d-1)(c-1).