To add matrices, we add the corresponding members.  The matrices must have the same dimensions.

example:

The matrices below show the voter turnout in River City, USA for the 1996 and 2000 Presidential elections.  By how many people did each precinct change from 1996 to 2000?

Using Identity and Inverse Matrices

The additive identity matrix for the set of all m × n matrices is the zero matrix, whose elements are all zeros.  The opposite, or additive inverse, of an m × n matrix A is –A.  –A is the m × n matrix with elements that are the opposites of the corresponding elements of A.

Find each sum.

Solving Matrix Equations

A matrix equation is an equation in which the variable is a matrix.  You can use the addition and subtraction properties of equality to solve matrix equations.

Solve for matrix X:

 

 

Finding Unknown Matrix Elements

example: Solve for the variables
Since the matrices are equal, the corresponding elements are equal. Use scalar multiplication on the first matrix, then write the sentences that show this equality.
By observation, x=3. So, by substitution, we can see y = 2.
Then, by substituting into the last equation we can find z.
The solution is:	(3, 2, 8)