Chapter6 Section 6.6 - Lesson

What You'll Be Learning

Find the determinant of a 2×2 or 3×3 matrix.
Solve a system of linear equations using Cramer’s Rule.

Read

Required Reading 6.6 - Systems of Linear Equations: Determinants

Watch, Take Notes, Self-check

Tip: Interactive Notes

Be a doer, not just a viewer! Check out the Video 26 guided notes to fill out as you watch.

Video 26 - Part 1: Finding Determinants of 2x2 Matrices

Check Your Understanding

Find the determinant of the matrix open square brackets table row cell negative 1 end cell 4 row 2 3 end table close square brackets

−11

Correct

5

Incorrect

−24

Incorrect

Video 26 - Part 2: Cramer’s Rule for Two Equations in Two Unknowns

Check Your Understanding

Use Cramer’s Rule to determine the solution of the following system of equations. Write your answer as a NON-SIMPLIFIED fraction.

LaTeX: 2x-4y=1

LaTeX: x+3y=-2

$open parentheses fraction numerator negative 5 over denominator 10 end fraction comma fraction numerator negative 5 over denominator 10 end fraction close parentheses$

Correct

$open parentheses fraction numerator 3 over denominator negative 6 end fraction comma fraction numerator 3 over denominator negative 6 end fraction close parentheses$

Incorrect

$open parentheses fraction numerator negative 2 over denominator 4 end fraction comma fraction numerator negative 2 over denominator 4 end fraction close parentheses$

Incorrect

$open parentheses fraction numerator 4 over denominator negative 8 end fraction comma fraction numerator 4 over denominator negative 8 end fraction close parentheses$

Incorrect

Video 26 - Part 3: Finding Determinants of 3x3 Matrices

Check Your Understanding

Find the determinant of A equals open square brackets table row cell negative 1 end cell 2 0 row 4 3 1 row 2 0 cell negative 3 end cell end table close square brackets

open vertical bar A close vertical bar equals 0

Incorrect

open vertical bar A close vertical bar equals negative 11

Incorrect

open vertical bar A close vertical bar equals 37

Correct

open vertical bar A close vertical bar space is undefined.

Incorrect

Video 26 - Part 4: Cramer’s Rule for Three Equations in Three Unknowns

Check Your Understanding

Use Cramer’s Rule to write the fraction that will determine y in the following system of equations.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 4 y plus z end cell equals 5 row cell x plus 3 y minus 2 z end cell equals cell negative 1 end cell row cell 7 y plus 3 z end cell equals 2 end table

The correct answer is shown below. If you finished solving for y, you will find y equals negative 11 over 65 .

y equals open vertical bar table row 2 5 1 row 1 cell negative 1 end cell cell negative 2 end cell row 0 2 3 row 2 cell negative 4 end cell 1 row 1 3 cell negative 2 end cell row 0 7 3 end table close vertical bar

Reminders & Tips

Cramer’s Rule is just one more method to solving systems of equations. The image below summarizes the different methods you have learned in this chapter, as well as mentioning the old methods of substitution/elimination/graphing that were learned in a previous course. Which way do you prefer?