February 25, 2021

To understand matrix equations, you should know how to multiply two matrices. Let's say you are showed the result of two matrices multiplication () and you are asked to find the matrix B and you are provided matrix A and C, how will you find it? With the help of the matrix equation. In a matrix equation, the unknown is a matrix. This means that you will denote the unknown matrix as **matrix X**.

**A · X = B**

To solve, check that the matrix is invertible, if it is, premultiply (multiply to the left) both sides by the matrix inverse of A.

If the equation is of type **X · A = B**, the members must postmultiply (multiply to the right) because matrix multiplication is not commutative.

1. Given the matrices . Solve the equation: A** ·** X = B

Find the determinant of the above matrix.

, this means that there is an inverse

2. Given the matrices . Solve the equation: X** ·** A + B = C

, this means that there is an inverse

3.Solve the matrix equation:

**A · X + 2 · B = 3 · C**

, this means that there is an inverse

4.Solve the matrix equation:

To solve a system of linear equations, it can be transformed into a matrix equation and then solved.