do now: solve the system of linear equations using matrices (row echelon form)
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Do Now: Solve the system of linear equations using matrices (Row Echelon Form)
1343
1
622
zyx
zyx
yx
Academy Algebra II/Trig12.3: Systems of linear equations: Determinants, 12.4: InversesUnit 3 Test: Thurs, 10/31 (12.1-12.4, 12.7)
Cramer's Rule
dc
ba
tc
sa
y
dc
ba
dt
bs
x ,
Cramer’s Rule can be used to solve a system of equations when the det = 0.
Given the system:
tdycx
sbyax
Using Cramer’s Rule, the solution to the system is given by:
12.4: Inverse Matrices
dc
baA
Two matrices are inverses of each other if their product = identity matrix.
The inverse of a 2x2 matrix is
ac
bd
AA
11
Note: Matrix A will not have an inverse ifthe determinant = 0.
Finding the Inverse for a 3 x 3You will find inverses for a 3 x 3 matrix on the calculator.
Input the following matrix by creating a new matrix or overwriting a current matrix.
Note: Once you are entering #’s in the cells for the matrix you can resize the matrix by selecting the Util menu (F6) – option 6.
1
340
431
011
Finding the Inverse for a 3 x 3
You will find inverses for a 3 x 3 matrixon the calculator.
Input the following matrix by creating a new matrix or overwriting a current matrix.Press Home.Type the name of your matrix and raise it to the -1 exponent. Press ENTER.
1
340
431
011
Finding the determinant on calculator
You can also find determinants for a matrixon the calculator.
To find the determinant for this matrix – on your home screen complete the following:Go to MATH menu (Press 2nd 5)Select Matrix, select det(Enter the name of your matrix, close parenthesis. Press ENTER.
340
431
011
Using inverse matrices to solve a linear system.
fdycx
ebyax
Given system:
f
e
y
x
dc
ba
BAX
f
e
dc
ba
y
x
BAX1
1