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

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

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4.4 Identity & Inverse Matrices

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

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

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

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

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

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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

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

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

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

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

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

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

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

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Solving Systems using Matrices and Inverses

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

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

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

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

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Ex. Solve

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Assignment

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