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Advanced Algebra Notes Sec. 3.8: Use Inverse Matrices to Solve Linear Systems

Advanced Algebra Notes Sec. 3.8: Use Inverse Matrices to Solve Linear Systems. Identity Matrix. For matrices, the n x n ______________________ is the matrix that has 1’s on the main diagonal and zero’s everywhere else. EX: 2 x 2 Identity 3 x 3 Identity. A.

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Advanced Algebra Notes Sec. 3.8: Use Inverse Matrices to Solve Linear Systems

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  1. Advanced Algebra Notes Sec. 3.8: Use Inverse Matrices to Solve Linear Systems Identity Matrix For matrices, the n x n ______________________ is the matrix that has 1’s on the main diagonal and zero’s everywhere else. EX:2 x 2 Identity 3 x 3 Identity A The multiplication of a matrix and an identity matrix (AI or IA) is always equal to _____. Two square matrices are _________of each other if their product (in both orders) is the n x nidentity matrix. EX: AB = I and BA = I The symbol used for the inverse of matrix A is ______. Inverses

  2. Inverse of a 2 x 2 Matrix If matrix A = , then provided 0. If |A| = 0, then A does not have an inverse. Example 1: Find the inverse of the matrix. Letter C we will use a graphing calculator to find the inverse. A) B) C) Skip! Calculator Problem.

  3. Example 2: Solve the matrix equation for x and solve a system using a matrix equation. A) First find the inverse of the matrix in front of x.

  4. B. Change one on Notes to this problem! Find the inverse.

  5. -2x + 3y = -11 5x + y = 19 C. Find the inverse: |A| = -2 -15 = -17 A-1 = = = = = (4, -1)

  6. 4x + 2y + 3z = 1 2x – 3y + 5z = -14 6x – y + 4z = -1 E. Skip for now! Calculator Problem (2, 1, -3)

  7. Lesson 3.8 Practice C 1-14 in the packet

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