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Algebra 2 3-6 Complete Lesson: Solving Systems Using Matrices

Last updated almost 4 years ago
23 questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
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Solve It! Is it possible to use the rules shown to change Figure 1 into Figure 2?

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Solve It! Resequence the following steps to change Figure 1 into Figure 2.

  1. Multiply row 2 by 2 and add it to row 3
  2. Divide row 2 by 8 and row 3 by -2
  3. Multiply row 3 by -1 and add it to row 1
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Problem 1 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 3 Got It?

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Problem 4 Got It? What is the solution of the system? Use an augmented matrix to solve and show your work on the canvas using colors that stand out. For efficiency, you may use the rectangle tool to represent matrix frames. The first frame for your augmented matrix is constructed for you as an example.

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Problem 4 Got It? Resoning: Which method is more similar to solving a system using row operations: elimination or substitution? Justify your reasoning.

A good, simple matrix rref calculator from the Linear Algebra Toolkit can be found here. Symbolab, WolframAlpha, and other utilities will also convert matrices into reduced row echelon form, but may require permium access to show all row operations. Desmos is also developing a matrix calculator!
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Problem 5 Got It?

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How many elements are in a 4 x 4 matrix? Enter only a number.

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Writing: Using Matrix A from Problem 1, recreated below, describe the difference between identifying element a21 and element a12.

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Open-Ended: Write a system of equations that can be modeled by the matrix.

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Review Lesson 1-5: Graph the inequality. Zoom and pan your graph to establish an appropriate viewing window.

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Review Lesson 1-5: Graph the inequality. Zoom and pan your graph to establish an appropriate viewing window.

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Review Lesson 2-6: Match each function with its transformation of y = x.

  • y = x + 2
  • y = 2x
  • vertical stretch by a factor of 2
  • vertical shift up 2 units
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Vocabulary Review: Select the correct word(s) to complete the sentence.

The partial solution of the system of equations at the left uses __?__.

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Use Your Vocabulary: Match each rref matrix from the left column with the solution it represents in the right column.

  • (0, 2, 3)
  • (2, 0, 3)
  • (2, 3, 0)
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Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

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Reflection: Math Success