Question

What is the method for solving for an elementary matrix such that AE=B, in the context of linear algebra?

Answer 1

To solve for an elementary matrix such that AE=B in the context of linear algebra, you should multiply both sides of the equation by the inverse of A on the left and simplify the equation to E = A^(-1)B.

Step-by-step explanation:

The method for solving for an elementary matrix such that AE=B in the context of linear algebra involves the following steps:

1. Multiply both sides of the equation AE=B by the inverse of A on the left.
2. This will give you the equation A^(-1)(AE) = A^(-1)B.
3. Since A^(-1)A will give you the identity matrix, you will be left with E on the left side of the equation.
4. Simplify the equation to E(E) = A^(-1)B.
5. Since E(E) is equal to E, you can write the equation as E = A^(-1)B.
6. Therefore, the elementary matrix E that satisfies the equation AE=B is equal to A^(-1)B.