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

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Last updated about 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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Question 1
1.

Solve It! Is it possible to use the rules shown to change Figure 1 into Figure 2?

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Question 3
3.

Problem 1 Got It?

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Question 4
4.

Problem 2 Got It?

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Question 5
5.

Problem 2 Got It?

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Question 6
6.

Problem 3 Got It?

Question 7
7.

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.

Question 8
8.

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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Question 9
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Problem 5 Got It?

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Question 10
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Question 11
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Question 12
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Question 13
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Question 14
14.

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

Question 15
15.

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

Question 16
16.

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

Question 17
17.

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

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.
Question 18
18.

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

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.
Question 19
19.

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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Question 20
20.

Vocabulary Review: Select the correct word(s) to complete the sentence.

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

Question 21
21.

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)
Question 22
22.

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.

Question 23
23.

Reflection: Math Success

Question 2
2.

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

  1. Multiply row 3 by -1 and add it to row 1
  2. Multiply row 2 by 2 and add it to row 3
  3. Divide row 2 by 8 and row 3 by -2