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MATRICES

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.

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MATRICES

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  1. MATRICES INVERSE MATRICES TO SOLVE LINEAR SYSTEMS

  2. 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.

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

  4. Inverse Matrices • Not all matrices have an inverse! • To find the inverse of a 2 x 2 matrix, first find the determinant. • 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.

  5. Inverse of a 2X2 Matrix

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

  7. Inverse Matrices Example 2:

  8. Solve a Matrix Equation

  9. Solve a Matrix Equation

  10. Solve a Matrix Equation

  11. Example of Inverse Matrices

  12. Example of Inverse Matrices

  13. Basketball Problem • 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.

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

  15. Basketball Problem

  16. Basketball Problem

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