About Gaussian Elimination:
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
#1:
Instructions: Solve each linear system using matrix methods.
a) $$-48y=20x - 8$$ $$-14 + 84y=-35x$$
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#2:
Instructions: Solve each linear system using matrix methods.
a) $$-6y + 2x=14$$ $$9x - 12=10y$$
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#3:
Instructions: Solve each linear system using matrix methods.
a) $$4x=26 - 10y$$ $$-6x=-12y - 12$$
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#4:
Instructions: Solve each linear system using matrix methods.
a) $$x - 1=-\frac{8}{7}y$$ $$10x=-5y + 10$$
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#5:
Instructions: Solve each linear system using matrix methods.
a) $$105 - 9x=6y$$ $$-5y=-41 - 8x$$
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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
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#2:
Solutions:
a) $$\left[ \begin{array}{cc|c}1&-3&7\\ 0&1&-3 \end{array}\right] $$
{(-2,-3)}
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#3:
Solutions:
a) $$\left[ \begin{array}{cc|c}1&\frac{5}{2}&\frac{13}{2}\\ 0&1&1 \end{array}\right] $$
{(4,1)}
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#4:
Solutions:
a) $$\left[ \begin{array}{cc|c}1&\frac{8}{7}&1\\ 0&1&0 \end{array}\right] $$
{(1,0)}
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#5:
Solutions:
a) $$\left[ \begin{array}{cc|c}1&\frac{2}{3}&\frac{35}{3}\\ 0&1&13 \end{array}\right] $$
{(3,13)}