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Warm-Up

Warm-Up. 1) Multiply. Show work. 3) Find the determinant by hand. 2) Multiply. Show work. 4) Find the determinant using your calculator. Daily Quiz – you may not use your notes. 1) Multiply. Show work. 3) Find the determinant by hand. 2) Multiply. Show work.

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Warm-Up

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  1. Warm-Up 1) Multiply. Show work. 3) Find the determinant by hand. 2) Multiply. Show work. 4) Find the determinant using your calculator.

  2. Daily Quiz – you may not use your notes. 1) Multiply. Show work. 3) Find the determinant by hand. 2) Multiply. Show work. 4) Find the determinant using your calculator.

  3. 4.4 Identity & Inverse Matrices

  4. Inverses What does “inverse” mean to you? What is the inverse of multiplication?

  5. Identity What does “identity” mean to you? What is the multiplicative identity for the real numbers? In other words, 5 * __= 5? The identity for multiplication is 1 because anything multiplied by 1 will be itself.

  6. What do we multiply by to get the identity? In other words, 5 * ___=1? a * a-1= 1 Any number multiplied by its inverse will be the identity.

  7. Identity Matrix Any matrix multiplied by its inverse will be the identity matrix. A * A-1= I A-1 *A = I 3x3 Identity Matrix 2x2 Identity Matrix

  8. Identity Matrix Just like 5*1 = 5… AI= A IA= A Or

  9. Ex. 1 Determine whether A and B are inverses. Find out if AB = I If so, then yes they’re inverses. If not, then no they’re not inverses. Use your calculator. YES

  10. Ex. 2 Determine whether A and B are inverses. YES

  11. Ex. 3 Determine whether A and B are inverses. NO

  12. The Inverse of a 2x2 Matrix A-1= As long as ad-cb =0 If ad-cd=0, then the matrix has no inverse!!!!

  13. Ex. 4 Find A-1, if it exists. A-1=

  14. Ex. 5 Find A-1, if it exists. A-1=

  15. Ex. 6 Find A-1, if it exists. Does not exist, because it’s not square.

  16. Ex. 7 Find A-1, if it exists.

  17. Questions????

  18. Solving Systems using Matrices and Inverses

  19. Solving Matrix Equations Suppose ax = b How do you solve for x? We cannot divide matrices, but we can multiply by the inverse. A-1 AX = B A-1 IX = A-1B X = A-1B

  20. Solving a Matrix Equation Solve the matrix equation AX=B for the 2x2 matrix X

  21. Step 1: find A-1 A-1= Step 2: Multiply both sides of the equation By A-1 on the left

  22. You can check the Solution by mult AX to see if you get B

  23. Ex. Solve

  24. Assignment

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