Multiplicative Inverses of Matrices and Matrix Equations

Young mathematicians so often have a love-hate relationship with matrices and their inverses. They love the idea of a quick algorithmic way to solve systems of equations, but get stuck in the arithmetic precision required by the method. This is where skill practice worksheets like this come in handy. Well-scaffolded sections contain a brief introduction that refreshes key steps and concepts for solving. No fancy bells or whistles here, just solid practice identifying, finding, and using inversions of 2x2 and 3x3 matrices.

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CCSS: Adaptable
Instructional Ideas

  • Clear and concise directions on this worksheet and answer key would provide a turnkey substitute lesson plan
  • Consider assigning problems to groups or pairs, having each member perform a step in turn and check one another's work
  • Break problems apart as bellringers or review problems after the topic is completed
Classroom Considerations

  • Answer key has color-coded steps that might need consideration if copying
  • Problem number 6 jumps from given to inverse in the answer key, where learners new to the idea are liable to need more intermediate steps spelled out
Pros

  • Problems are well-explained and build in complexity through the worksheet
  • Numbers chosen work out to integer solutions, allowing the focus to be on manipulating matrices instead of arithmetic
  • Included answer key also shows several intermediate steps
Cons

  • Second additional resource Matrix Inverses and Solving Matrix Equations is linked to a worksheet on modeling quadratic functions that doesn't seem to fit with this lesson