Solving Systems with Matrices – Using Graphing Calculator
1. Using your calculator, find the inverse of the following:
4 11
a) A = 

1 3 
-1
A =
2 4 3 


b) B = 1 0  1


5 2  2
B-1=
2. Using the results from above, find
a) A-1A
b) B-1B
3. For each of the following systems,
a) write each system as a matrix equation
b) find the inverse of the coefficient matrix
c) solve the matrix equation
d) substitute to check your solutions
a) x + 2 y = 2
2x+5y =3
b) 4 x + 3 y = 9
x + y = 8
d) 50 x + 30 y + 10 z = 19
80 x + 20 z = 23.40
10 x + 40 y + 60 z = 48.30
c) 3 x - 2 y = 1
-4x + 3 y = 11
e) 0.18 c + 0.24 u + 0.72 b = 33.54
1u - 2b = 0
1 c + 1 b = 39
4. During July, stock X gained or lost x dollars in value per share, stock Y, y dollars in value per share, and
stock Z, z dollars in value per share. On stocks X, Y, and Z, three shareholders realized the following losses or
gains during July. Find x, y, and z (which represent the amount gained or lost in value per share).
Shareholder
McWilliams
Baswick
Siena
Shares of X
100
60
90
Shares of Y
150
110
40
Shares of Z
80
70
100
Gain/Loss
-$170
-$140
$160
5. The sum of three numbers is 8. The second number is 4 less than three times the first. The third
number is 7 more than twice the first added to the second. Find the three numbers.
6. Jamie, Paul, and Anne all got prime jobs out of university. They met to discuss their starting salaries. Paul
is making $1000/year more than Anne. Jamie is making 80% of the other two salaries combined. In total, the
three make a combined annual salary of $99990. Find their salaries.