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Unit 1.11 – Use Inverse Matrices to Solve Linear Systems

Unit 1.11 – Use Inverse Matrices to Solve Linear Systems. Unit 1 – Algebra: Linear Systems, Matrices, & Vertex-Edge Graphs. 1.11 – Use Inverse Matrices to Solve Linear Systems Georgia Performance Standard: MM3A4b

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Unit 1.11 – Use Inverse Matrices to Solve Linear Systems

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  1. Unit 1.11 – Use Inverse Matrices to Solve Linear Systems

  2. Unit 1 – Algebra: Linear Systems, Matrices, & Vertex-Edge Graphs • 1.11 – Use Inverse Matrices to Solve Linear Systems • Georgia Performance Standard: • MM3A4b • Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology. • MM3A5a • Represent a system of linear equations as a matrix equation. • MM3A5b • Solve matrix equations using inverse matrices

  3. Vocabulary • The n x nidentity matrix is a matrix with 1’s on the main diagonal and 0’s elsewhere. If A is any n x n matrix and I is the n x n identity matrix, then AI = A and IA = A. 3 x 3 Identity Matrix 2 x 2 Identity Matrix

  4. Vocabulary • Two n x n matrices A and B are inverses of each other if their product (in both orders) is the n x n identity matrix. That is, AB = I and BA = I. An n x n matrix A has an inverse if and only if det A ≠ 0. The symbol for the inverse of A is A-1

  5. Inverse of 2 x 2 Matrix • Steps: • Same as finding the determinant just put it under 1. • Flip and Negatify! (Math word…sort of)

  6. Example for finding the inverse of a 2 x 2 matrix…

  7. Try this… • Page 54: 1-3 • Guided Practice

  8. Solve a Matrix Equation • Steps: • Find the inverse of the matrix that is next to the variable. • Multiply both sides of the equation by the inverse • Left side will cancel

  9. Example

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