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Grade 11 · Math · Algebra 2

11th grade Solve a system with matrix inverses or augmented matrices worksheet

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solve a system with matrix inverses or augmented matrices

Grade 11 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

  1. [1, 3, -2 | 5; 2, -1, 4 | 9; -3, 2, 1 | 7]. Luz replaces row 2 of the table in the figure with row 2 − 2 × row 1. What is the new number in row 2, in column 3?

  2. [2, 1, 3 | 6; 0, 1, -2 | 4; 0, 3, 2 | -5]. Noah replaces row 3 of the table in the figure with row 3 − 3 × row 2. What is the new number in row 3, after the bar?

  3. Adult volunteers sold 200 school-play tickets for $1,160: student tickets at $4 and adult tickets at $7. Zee uses X = A⁻¹B. How many student tickets were sold?

  4. Jun lays 30 tiles covering 66 square inches: x square tiles of 4 square inches and y triangle tiles of 1 square inch. Using X = A⁻¹B, how many square tiles?

  5. The cooking club spends $26 of club funds on 9 bags: rice at $2 a bag and beans at $4 a bag. Using X = A⁻¹B, how many bags of rice does Kira buy?

  6. Read this first

    System

    3x + 2y = 2; 2x + 2y + z = 4; -x − y − z = -5. Number table A = [3, 2, 0; 2, 2, 1; -1, -1, -1], B = [2; 4; -5].

  7. Luz's calculator gives A⁻¹ = [1, -2, -2; -1, 3, 3; 0, -1, -2] for the system in the figure. What is z?

  8. System

    2x + 2y + 3z = 16; 3x + y + 3z = 24; -y − z = -1. Number table A = [2, 2, 3; 3, 1, 3; 0, -1, -1], B = [16; 24; -1].

  9. Milo's calculator gives A⁻¹ = [2, -1, 3; 3, -2, 3; -3, 2, -4] for the system in the figure. What is x?

  10. System

    2x + z = 14; 3x + y + z = 15; -x − z = -10. Number table A = [2, 0, 1; 3, 1, 1; -1, 0, -1], B = [14; 15; -10].

  11. Noah's calculator gives A⁻¹ = [1, 0, 1; -2, 1, -1; -1, 0, -2] for the system in the figure. What is z?

  12. System

    -x + 2y + 2z = 3; x − y = -2; -x + y − z = 4. Number table A = [-1, 2, 2; 1, -1, 0; -1, 1, -1], B = [3; -2; 4].

  13. Pia's calculator gives A⁻¹ = [1, 4, 2; 1, 3, 2; 0, -1, -1] for the system in the figure. What is y?

  14. System

    3x + y = 1; -y − z = -8; -x − y − z = -6. Number table A = [3, 1, 0; 0, -1, -1; -1, -1, -1], B = [1; -8; -6].

  15. Ren's calculator gives A⁻¹ = [0, 1, -1; 1, -3, 3; -1, 2, -3] for the system in the figure. What is x?

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11th grade Solve a system with matrix inverses or augmented matrices worksheet – printable
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About this worksheet

Solve a system with matrix inverses or augmented matrices. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can write a system as a matrix equation AX = B, one row per equation and one column per letter.
  • I can solve a system with X = A⁻¹B, using a given inverse or one I find.
  • I can do a row step on an augmented table and read the answer from the last table.

Words to know

coefficient matrix, A: The table of the numbers in front of the letters.

matrix equation: AX = B: the table A times the letter column X gives B.

row step: Replace a row with itself minus a multiple of another row.

back-substitution: Use the last row's answer in the row above it.

X = A⁻¹B: Multiply B by the inverse, a row of A⁻¹ against B.

Common mistakes

Multiplied B by the columns of the inverse (B times A⁻¹) instead of each row of the inverse times B. Say it together: X = A⁻¹B, a row of A⁻¹ against the column B.

Multiplied by the matrix A itself instead of its inverse.

Left out the 1/det in front of the inverse, so the answer came out det times too big. Ask what number sits in front of A⁻¹.

What to say

Ask: which table undoes A?

Questions parents ask

What is the most common mistake with solve a system with matrix inverses or augmented matrices?

Multiplied B by the columns of the inverse (B times A⁻¹) instead of each row of the inverse times B. Say it together: X = A⁻¹B, a row of A⁻¹ against the column B.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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