Download 4.5 Solving Systems using Matrix Equations and Inverses

OBJ: To solve systems of linear
equations using inverse matrices &
use systems of linear equations to
solve real-life problems
4.5 Solving Systems using
Matrix Equations and Inverses
5x  4 y  8
1x  2 y  6
A linear system can be written as a matrix
equation AX=B
5  4  x  8
1 2   y   6

   
Constant
Coefficient
matrix
Variable
matrix
matrix
Ex 1: Write as a matrix equation
3x  4 y  5
2 x  y  10
 3
2

4  x  5 





 1  y   10
DO NOT COPY
Solving Matrix Equations
Suppose 8x = 24
How do you solve for x?
We cannot divide
matrices, but we can
multiply by the
inverse.
A-1 AX =A-1 B
IX = A-1B
X = A-1B
Ex 2: Solve using matrices
3x  4 y  5
2 x  y  10
 3 4   x   5 
 2  1  y    10

  

AX = B
X = A-1B
x = -7
A
B
y = -4
(-7, -4)
Ex 3: Solve 7 x  3 y  11
14 x  4 y  2
x = 5/7
y=2
(5/7, 2)
Ex 4: Solve using matrices
2 x  3 y  z  1
3x  3 y  z  1
2 x  4 y  z  2
x=2
y = -1
z = -2
(2, -1, -2)
Ex 5: Solve using matrices
 x  3 y  5z  15
2x  y
1
9 x  8 y  4 z  12
x=4
y = -7
z=2
(4, -7, 2)