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6.4 and 6.5

6.4 and 6.5. 6.4 Inverse Matrices 6.5 Determinants and Cramer’s Rule. Inverse Matrix Obj: find an inverse matrix to solve a system. Multiplicative Identity Multiplicative Inverse Identity Matrix Inverse Matrix. Find the Inverse. Calculator Steps.

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6.4 and 6.5

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  1. 6.4 and 6.5 6.4 Inverse Matrices 6.5 Determinants and Cramer’s Rule

  2. Inverse MatrixObj: find an inverse matrix to solve a system • Multiplicative Identity • Multiplicative Inverse • Identity Matrix • Inverse Matrix

  3. Find the Inverse

  4. Calculator Steps • 3x3 or larger will be done with the calculator. • Enter the matrix • Go to the home screen • Name the matrix Inverse button Enter Enter

  5. Using the Inverse • Given a system, use the inverse matrix to solve. • Rewrite the system as a matrix equation. =

  6. Practice Solve the system of equations by using inverse matrix methods.

  7. 6.5 DeterminantsObj: find the determinant to solve a system Every square matrix has a number associated with it that is called a DETERMINANT. To find the determinant of a 2x2 matrix, multiply the diagonals and subtract the products. 18 – 8 = 10

  8. Find the Determinant of a 3x3 • Expand by cofactors • Expand by row 1 5 1 -1 -(-3) -2 -1 +(-1) -2 1 0 2 1 2 1 0 = 5 (2 – 0) – (-3)(-4 – (-1)) + (-1)(0 – 1)

  9. Calculator Steps Enter the matrix 2nd Quit Matrix Math det( Matrix Name Enter Enter

  10. Cramer’s Rule • Another way of solving a system of equations using determinants. • It is a way to find one answer at a time. Write the coefficient matrix. To solve for x, replace the x column with the constant column. Divide by the coefficient matrix. To solve for y, replace the y column with the constant column. Divide by the coefficient matrix.

  11. Practice Find y for the system of equations.

  12. Assignment • 6.4 1 – 41 e.o.o. • 6.5 1 – 41 e.o.o., 53

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