Find the determinate of both of the following matrices.

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Finding the Inverse of a Matrix

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Presentation transcript:

Find the determinate of both of the following matrices.

Section 4-7

What does it mean for two matrices to be inverses of each other? Two matrices are inverses of each other if their product is the identity matrix when multiplied in any order. Identity matrix = or

Multiply these matrices both ways. Are they inverses of each other?

How do you find the inverse of a matrix? Step 1: Find the determinate of the matrix. Step 2: Find the reciprocal of the determinate. Step 3: Multiply the reciprocal of the determinate by a and d switch places b and c change signs

Find the inverse of the following matrix. Step 1: Find the determinate of the matrix. Step 2: Find the reciprocal of the determinate. Step 3: Multiply the reciprocal of the determinate by

Step 1: Find the determinate of the matrix. Step 2: Find the reciprocal of the determinate. Step 3: Multiply the reciprocal of the determinate by

How can you check your work? 1. Multiply the original matrix by your answer. You should get the identity matrix if you are correct. or 2. Use calculator

Working with matrices on a TI-83 To INPUT a matrix: 1. 2 nd  Matrix 2. Use arrows to scroll over to EDIT, press ENTER 3. Type in the dimensions of your matrix pressing enter after each number (Remember: row then column) 4. Type in each entry of the matrix, pressing ENTER after each one to move to the next entry. 5. When finished, press 2 nd  Quit

Working with matrices on a TI-83 To find the inverse of a matrix: (after inputting the matrix) 1. 2 nd  Matrix 2. Use arrows to pick the matrix you want to find inverse of, press ENTER 3. Press the X -1 button, then ENTER

Working with matrices on a TI nd  Matrix 2. Use arrows to pick the matrix you want to use, press ENTER 4. 2nd  Matrix To perform operations with matrices: (after inputting the matrix) 5. Use arrows to pick the matrix you want to use, press ENTER 3. Type in operation sign wanted.

Working with matrices on a TI-83 Use your calculator to check your answer for the inverse of:

A few more things about matrices and inverses. Only square matrices have inverse. If a matrix’s determinant is 0, then it does not have an inverse.

P199 #10, 12, 20, 22, 24 CHECK you answers with your calculator. You must know how to do the work by hand. We will go over the answers in _________ minutes.

P199 #10, 12, 20, 22, yes 12. no The inverse does not exist because the determinate is 0.