2.5 – Determinants and Multiplicative Inverses of Matrices

 Determinant: a real number representation of a matrix ◦ Denoted as det or

 Square Matrix – a matrix with equal number of rows and columns. You can only find determinants of these.  Singular – when a matrix has a zero determinant.  Invertible/Nonsingular – a matrix that has non-zero determinant

Let A be an m x n matrix. If there exists a matrix A -1 such that AA -1 = I n = A -1 A Then A -1 is called the inverse of A. A -1 is read “A inverse.” I n is called the identity matrix – the main diagonal has 1’s and the rest of the entries are 0.

Multiply these two matrices. (FYI… they are inverses of each other)

Let then

 P 588 #10, 11, 30 – 36 (even)

If A is an invertible matrix, the system of linear equations represented by AX = B has a unique solution: X = A -1 B