MATRICES INVERSE MATRICES TO SOLVE LINEAR SYSTEMS Identity

MATRICES INVERSE MATRICES TO SOLVE LINEAR SYSTEMS

Identity Matrices § § An identity matrix is a square matrix that has 1’s along the main diagonal and 0’s everywhere else. When you multiply a matrix by the identity matrix, you get the original matrix.

Inverse Matrices § When you multiply a matrix and its inverse, you get the identity matrix.

Inverse Matrices § § Not all matrices have an inverse! To find the inverse of a 2 x 2 matrix, first find the determinant. a) § If the determinant = 0, the inverse does not exist! The inverse of a 2 x 2 matrix is the reciprocal of the determinant times the matrix with the main diagonal swapped and the other terms multiplied by -1.

Inverse of a 2 X 2 Matrix n

Inverse Matrices Example 1: det(A) = 3(2) – (-5)(-1)

Inverse Matrices Example 2:

Solve a Matrix Equation n

Solve a Matrix Equation n

Solve a Matrix Equation n

Example of Inverse Matrices n

Example of Inverse Matrices n

Basketball Problem n During the 2003 -2004 NBA season, Dirk Nowitzki of the Dallas Mavericks made a total of 976 shots and scored 1680 points. His shots consisted of 3 -point field goals, 2 -point field goals, and 1 -point free throws. He made 135 more 2 -point field goals than free throws. Use an inverse matrix to find how many of each type of shot he made.

Basketball Problem n n n x = 3 -point field goals y = 2 -point field goals z = 1 -point free throws x + y + z = 976 shots 3 x + 2 y + z = 1680 points y – z = 135

Basketball Problem n

Basketball Problem n