Objective: Students will solve systems of equations using inverse matrices.

AX = B A= Coefficient Matrix X = Matrix of Variables B= Matrix of Constants Write the following as a matrix equation:

You can solve for the Matrix of Variables by multiplying EACH side of the matrix by A -1 on the left.

1.2.

Solution: (x, y, z)  Graph: (-2, 3, -4) 3 different unknowns in a system of 3 variables

Matrix-MATH-rref-enter – quit-matrix, call up the matrix you want rref([A]) (rref= reduced row echelon form) Answers are in the last column. Other rows contain 1’s along main diagonal and 0’s below

In the 1968 presidential election, 538 electoral votes were cast. Of these x went to Richard Nixon, y went to Hubert Humphrey and z went to George Wallace. The value of x is 110 more than y. The value of y is 145 more than z. Write a system of equations and solve to find out how many votes each candidate received.

The senior class is selling boxed greeting cards. Birthday cards sell for $5.00 a box, while thank you cards sell for $7.00 a box. You sold 4 more boxes of birthday cards than thank you cards; your total sales amounted to $152. How many boxes of each kind did you sell? Write a system of equations and solve using inverse matrices.

You have $10,000 to invest in two types of stock. The expected annual returns for the stocks are; 10% for stock A and 6% for stock B. You want the overall annual return to be 8%. Write a linear system of equations that represents the given information. Write a matrix equation and solve to find out how much you should invest in each type of stock.