Post on 31-Mar-2015
Determinant
222122
11
22
11 or det bababa
ba
ba
ba
The numerical value of a square array of numbers that can be used to solve systems of equations with matrices.
Second-Order Determinant(of a 2 x 2 Matrix)
The word with the matrix
symbol
The Determinant symbol
222122
11
22
11 or det bababa
ba
ba
ba
(Criss-Cross & multiply then subtract)
Example 1
204768 204768 204768 204768
nth-Order Determinant
The determinant of any n x n (square) matrix
Third-Order Determinant(of a 3 x 3 Matrix)
Determinant of what’s leftDeterminant of what’s leftDeterminant of what’s leftSigns alternate, beginning with minus
Then simplify
Example 2
34)3)(1( 34)3)(1(
Select any row & column, then calculate the determinant with
expansion of the minors
34)3)(1(
Identity Matrix for Multiplication
A square matrix, that when multiplied with another square matrix, results in a matrix with no change.The square matrix always consists of 1’s on the diagonal beginning with the first element; the remaining elements are zeros.
100
010
001
10
01
Inverse Matrix (A-1)
A matrix that when multiplied by another matrix results in the identity matrix.
IAA 1
Note: Not all matrices have an inverse – If the determinant of the original matrix has a value of
zero, A-1 does not exist
Example 3
Determine if a matrix exists (Det ≠ 0)
423
-4
Switch places
Same place
Switch Signs
The inverse is used to solve systems of equations with matrices.
11
32
53112
Calculate the determinant:
Determine the inverse:
Multiply each side of the matrix equation by the inverse & solve:
Example 5
)(085.06.10. yxyx
Define the variables:
Let x = amount of 10% bondLet y = amount of 6% bond
Two variables, two equations:x + y = 10,500
Simplify; no decimals.
Write matrix equation: Determine the inverse:
53
111(-5) – 3(1) = -8
3x – 5y = 0
HW: Page 102