Upload
eleanor-clarke
View
243
Download
2
Tags:
Embed Size (px)
Citation preview
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.
When you multiply a matrix by the identity matrix, you get the original matrix.
1 0 0
0 1 0
0 0 1
1 0
0 1
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.
Determinants
• **To find a determinant you must have a SQUARE MATRIX!!**
For the square matrix A = , the determinant is written as detA, or as det and it’s value is det = ad - bc .
Examples!
Find the determinant:
1. 5 7
11 8 5 8 7 11 40 77
37 40 77
2. 3 2
1 5 3 5 2 1 15 2
1715 2
3. 10 2
0 310(-3) - (-2)(0)
-30 + 0 = -30
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.
4.
2 3 8
6 7 1
4 5 9
Finding a 3x3 determinant is 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.
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 =
For the square matrix A =
54
32
Find the determinant, the inverse matrix A-1, and show that A A-1 = I .
Example
Solution
detA = det
54
32 = (2 5) - (3 4) = 10 - 12 = -2
24
352
1
12
5.15.2A-1 = =
54
32
12
5.15.2
))1(5()5.14()25())5.2(4(
))1(3()5.12()23())5.2(2(
10
01
AA-1 =
Solution Continued
¿
¿
You try!
Find the determinant, the inverse, and prove the
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.
Homework:
Inverses worksheet, all problems.
http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-5/4_5HW.pdf