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Warm Up

Warm Up. Inverse Matrices. Three main topics today. Identity Matrix Determinant Inverse Matrix. Identity Matrices. An identity matrix is a square matrix that has 1’s along the main diagonal and 0’s everywhere else.

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Warm Up

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  1. Warm Up

  2. Inverse Matrices

  3. Three main topics today • Identity Matrix • Determinant • Inverse Matrix

  4. Identity Matrices • An identity matrix is a square matrix that has 1’s along the main diagonal and 0’s everywhere else. • When you multiply a matrix by the identity matrix, you get the original matrix.

  5. Determinant • The determinant of a square matrix is a constant value that doesn’t have much meaning on its own, but finding it allows us to do other things with matrices. • We will find determinants of 2x2 matrices by hand, and anything bigger on the calculator.

  6. Determinants • **To find a determinant you must have a SQUARE MATRIX!!** For the square matrix A =, the determinant is written as detA, or as detand it’s value is det= ad - bc.

  7. Examples!

  8. Find the determinant:

  9. As stated before, this value of -30 doesn’t really do anything for us on its own, but we will see how we can use this value later.

  10. Finding a 3x3 determinantis a pain to do by hand, we wil use the calculator for these. • Enter this matrix into your calculator for matrix [A] • Go back to homescreen • Select Matrix ---Math---det( • Select matrix ----Names----[A]---- Enter.

  11. Inverse Matrix (A-1) • The product of any square matrix A and its inverse matrix A-1 is equal to the identity matrix I. We can write this as A A-1 = A-1A = I For the square matrix A =the inverse is written as A-1 =

  12. Example For the square matrix A = Find the determinant, the inverse matrix A-1, and show that A A-1 = I .

  13. Solution detA = det = (2  5) - (3  4) = 10 - 12 = -2 A-1 = =

  14. Solution Continued AA-1 =

  15. You try! Find the determinant, the inverse, and prove the

  16. Inverses of larger matrices (3x3): We will do this on the calculator • Enter the matrix under edit • Go to home screen • Select Matrix, then select the corresponding letter to your matrix. Hit enter. • Press the button. Hit enter.

  17. Homework: Inverses worksheet, all problems. http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-5/4_5HW.pdf

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