We previously learned how to solve a system of linear equations using graphing, substitution, and elimination. Now we will move on and learn how to perform this task using a matrix. A matrix is an ordered array of numbers. We can transform our matrix using row operations to gain a solution for our system.

Test Objectives
• Demonstrate the ability to set up an augmented matrix
• Demonstrate the ability to place a matrix in row echelon form
• Demonstrate the ability to solve a linear system using matrix methods
Gaussian Elimination Practice Test:

#1:

Instructions: Solve each linear system using matrix methods.

a) $$-48y = 20x - 8$$ $$-14 + 84y = -35x$$

#2:

Instructions: Solve each linear system using matrix methods.

a) $$-6y + 2x = 14$$ $$9x - 12 = 10y$$

#3:

Instructions: Solve each linear system using matrix methods.

a) $$4x = 26 - 10y$$ $$-6x = -12y - 12$$

#4:

Instructions: Solve each linear system using matrix methods.

a) $$x - 1 = -\frac{8}{7}y$$ $$10x = -5y + 10$$

#5:

Instructions: Solve each linear system using matrix methods.

a) $$105 - 9x = 6y$$ $$-5y = -41 - 8x$$

Written Solutions:

#1:

Solutions:

a) $$\left[ \begin{array}{cc|c} 1&\frac{12}{5}&\frac{2}{5}\\ 0&0&0 \end{array} \right]$$

Infinite number of solutions

#2:

Solutions:

a) $$\left[ \begin{array}{cc|c} 1&-3&7\\ 0&1&-3 \end{array} \right]$$

{(-2,-3)}

#3:

Solutions:

a) $$\left[ \begin{array}{cc|c} 1&\frac{5}{2}&\frac{13}{2}\\ 0&1&1 \end{array} \right]$$

{(4,1)}

#4:

Solutions:

a) $$\left[ \begin{array}{cc|c} 1&\frac{8}{7}&1\\ 0&1&0 \end{array} \right]$$

{(1,0)}

#5:

Solutions:

a) $$\left[ \begin{array}{cc|c} 1&\frac{2}{3}&\frac{35}{3}\\ 0&1&13 \end{array} \right]$$

{(3,13)}