1. Solving Matrix equations
Exercise 7C

2. Solving Matrix equations
To Solve matrix equations you need to find:
the inverse of you matrix
Know what the Identity Matrix is
and how do we use these two principles together to solve a matrix equation.

3. What is an Identity Matrix?
The unit matrix, previously defined as a significant square matrix, does not alter any other matrix by which it is multiplied. It is denoted by I and is known as the multiplicative identity matrix.
Thus, it follows that AI = IA = A, if A is a square matrix.

4. What is the Inverse (2X2) Matrix?
Only square matrices have inverses. If , then its inverse A−1 equals
Step 1: Find the Determinant - (ad − bc) written as det (A) or | A |
Step 2: Rearrange the Matrix layout -
Only used in (2x2) matrix!!!!
Notice that if det (A) = 0, the inverse does not exist, as is undefined. In this case, matrix A is called a singular matrix
Swap
Sides
X -1

5. What Happens If I multiply the Inverse by the original matrix
When any square matrix is multiplied by its inverse we obtain the identity, I. The inverse of matrix A is written as A−1. By definition: A × A−1 = A−1 × A= I.
if A is a (2 × 2) matrix, then:
if A is a (3 × 3) matrix, then:

6. Example

7. Answer

8. Where can we Use this method????
We can use this method to solve linear simultaneous equations!
The simultaneous equations may be expressed as the matrix equation.

10. Example

11. Answer