Unit 10 Matrices Revisited

Lesson 1

Learning Focus

Extend strategies for solving systems in two variables to solve systems in $n$ variables.

Lesson Summary

In this lesson, we reviewed strategies for solving systems of equations and extended them to solve systems with more that $2$ variables. We focused specifically on the process of using matrices and row-reduction to solve systems.

Lesson 2

Learning Focus

Use matrix multiplication in context.

Lesson Summary

In this lesson, we reviewed the row-by-column procedure for multiplying matrices, and used matrix multiplication to model a context.

Lesson 3

Learning Focus

Examine properties of matrix addition and multiplication.

Lesson Summary

In this lesson, we compared the properties of matrix addition and multiplication with the properties of addition and multiplication of real numbers, such as the associative properties, the commutative properties, and properties of identities and inverses. We found a lot of similarities, and some differences, and learned that we can find matrices that behave like $0$ and $1$ in the real number system.

Lesson 4

Learning Focus

Examine a new strategy for finding the multiplicative inverse of a matrix.

Lesson Summary

In this lesson, we learned a second method for finding the multiplicative inverse of a $2 \times 2$ matrix. We also found ways to determine if a $2 \times 2$ matrix has a multiplicative inverse or not.

Lesson 5

Learning Focus

Use multiplicative inverse matrices to solve systems.

Lesson Summary

In this lesson, we learned a new method for solving systems of equations by representing the system with a matrix equation and using multiplicative inverse matrices to solve the equation. The solution to the matrix equation provides the solutions to the system.

Lesson 6

Learning Focus

Solve $n \times n$ systems of linear equations.

Lesson Summary

In this lesson, we extended the method of solving systems by using matrix equations and the multiplicative inverse to $n \times n$ systems of equations. We used technology to find the multiplicative inverse matrix.