You have probably noticed that when a matrix has no inverse, one of the rows is a multiple of another row. For a 2 ( 2 matrix, this also means that the products of the diagonals are equal, or that the difference of these products is 0.

This difference of the diagonals is called the determinant of the matrix. For any
2 ( 2 matrix

The determinant is ad - bc.
Make up some 2 ( 2 matrices that have a determinant with value 1. Find the inverses of these matrices. Describe the relationship between the entries of each matrix and its inverse matrix.
Make up some 2 ( 2 matrices that have a determinant with value 2. Find the inverses of these matrices. Describe the relationship between the entries of each matrix and its inverse matrix.
Write a conjecture about the inverse of a matrix and how it relates to the determinant. Test your conjecture with several other 2 ( 2 matrices. Does your conjecture hold true regardless of the value of the determinant?

Transcribed Image Text:

i8 18-18 18 4