Reflection: Connection to Prior Knowledge Solving Systems of Equations using Inverse Matrix Operations - Section 2: Explanation


Depending on how well students retained their knowledge of matrix multiplication from earlier in the unit lesson, I may review this topic as we learn to use inverse matrices to solve systems. Since we represent our matrix equation with the (coefficient matrix)(variable matrix)=(constant matrix) we will always multiply by the coefficient matrix on the front of the left side of the equation and thus we must always place the inverse coefficient matrix on the front end of the right side of the equation. (i.e., between the equal sign and the constant matrix)   I would recommend having a student summarize/review this, too, so that the kids can hear this in someone else’s words, too. It will be a good opportunity for students to engage in mathematical practices (MP3, MP6).

A good topic to discuss in this lesson is why the commutative property doesn’t hold for matrices, and, how this affects the process used when using matrices to solve systems of linear equations (MP2).

  Connection to Prior Knowledge: Reviewing Matrix Multiplication
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Solving Systems of Equations using Inverse Matrix Operations

Unit 10: Matrices
Lesson 7 of 12

Objective: SWBAT model a system of equations using matrices and solve for the unknowns using inverse matrices.

Big Idea: Students find their love for matrices when they learn how much easier solving systems of equations can be!

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inverse matrices and systems
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