Systems of Equations and Inequalities: Matrices and Determinants

Adding and Subtracting Matrices

Matrices can be added and subtracted just like numbers and like variables. The trick is that the matrices must have the same number of rows and columns or they must have the same dimensions. If they do not, then we can't perform addition or subtraction. The sum or difference of two matrices is the sum or difference of corresponding entries.

For example, suppose A = two rows and two columns, row one has a sub 1 1, a sub 1 2, row two has a sub 2 1, a sub 2 2 and B = two rows and two columns, row one has b sub 1 1, b sub 1 2, row two has b sub 2 1, b sub 2 2...

...then A + B = two rows and two columns, row one has a sub 1 1 plus b sub 1 1, a sub 1 2 plus b sub 1 2, row two has a sub 2 1 plus b sub 2 1, a sub 2 2 plus b sub 2 2


Notice that the resulting matrix has the same dimensions as the two original matrices.

Subtraction will work the same but you will be subtracting corresponding entries.