Applying Matrices to Linear Systems
Matrix addition and matrix multiplication have many of the properties of ordinary addition and multiplication.
An important exception to the similarity of these properties is that matrix multiplication is not commutative: in general AB ≠ BA. Since products cannot commute, left multiplication can give a different product from right multiplication.
Before discussing other properties, we first need to identify some important matrices.
Any m x n matrix whose elements are all zero is called a zero matrix.
A square matrix is any matrix having the same number of column and rows.
The identity matrix, written I, is a square matrix where all the elements are 0 except the principal diagonal which has all ones
A diagonal matrix is a square matrix that has zeroes everywhere except along the main diagonal (top left to bottom right).
Learn more about applying matrices to linear systems by reading the explanation below.
Applying Matrices to Linear Systems
Practice: Find the additive inverse of a 2x2 matrix in the following exercises.