1. You have three employees, whose salaries are 8, 10, and 15 dollars per hour. Working alone, they can bake and decorate cakes at rates of 3, 7, and 12 cakes per hour (respectively). An order comes in for 184 cakes, to be delivered tomorrow (in 24 hours), and you will ...

Matrix inverses can be used to solve linear systems

Gauss-Jordan matrix reduction

1. Construct a matrix representation of the following system of equations, and solve it using the matrix:

$$ \begin{eqnarray} -3x + 6y - 9z &=& 3\\ x - y - 2z &=& 0\\ 5x + 5y - 7z &=& 63 \end{eqnarray} $$

Solution: $$ x = 8, y = 6, z = 1 $$

1. Write clear sentences explaining how you can tell:
   1. Whether it is possible to multiply two matrices together.
   2. What the size of the resulting matrix will be.
2. Solve the following system of equations (find the intersection of the two lines):

$$ \begin{eqnarray} 2x + 3y & = & 7 \\ -2x - 5y & = & 11 \end{eqnarray} $$

3. Using ...