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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

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  1. Zee writes the system 3y + 2x = 8 and x − 4y = 1 as AX = B. Which matrix equation is it?

    • [2, 3; 1, -4][8; 1] = [x; y]
    • [2, 3; 1, 4][x; y] = [8; 1]
    • [2, 3; 1, -4][x; y] = [8; 1]
    • [3, 2; 1, -4][x; y] = [8; 1]
    • [2, 1; 3, -4][x; y] = [8; 1]

  2. 3x + 5y = 13; x + 4y = 2. Number table A = [3, 5; 1, 4]. Pia solves the system in the figure with X = A⁻¹B, where A⁻¹ = (1/7)[4, -5; -1, 3] and B = [13; 2]. What is x?

  3. Esme replaces row 2 of [1, 3 | 7; 4, 5 | 6] with row 2 − 4 × row 1. What is the new number in row 2, after the bar?

  4. Pia solves 2x + 5y = 16 and x + 3y = 10 with X = A⁻¹B. What is y?

  5. Ren solves 3x + 4y = 5 and 2x + 5y = 8 with X = A⁻¹B. What is x?

  6. Tala solves 4x + y = 5 and 3x + 2y = 0 with X = A⁻¹B. What is y?

  7. Read this first

    Start

    [1, 2, -1 | 7; 2, 5, 1 | 24; 1, 5, 9 | 39]. Row steps: row 2 − 2 × row 1, then row 3 − row 1, then row 3 − 3 × row 2.

  8. Tala row-reduces the system in the figure to the last table [1, 2, -1 | 7; 0, 1, 3 | 10; 0, 0, 1 | 2]. What is y?

  9. Start

    [1, 1, 2 | 11; 3, 4, 3 | 16; 2, 3, 2 | 10]. Row steps: row 2 − 3 × row 1, then row 3 − 2 × row 1, then row 3 − row 2.

  10. Zee row-reduces the system in the figure to the last table [1, 1, 2 | 11; 0, 1, -3 | -17; 0, 0, 1 | 5]. What is y?

  11. Start

    [1, 2, -1 | 5; 4, 9, -1 | 32; 3, 8, 4 | 41]. Row steps: row 2 − 4 × row 1, then row 3 − 3 × row 1, then row 3 − 2 × row 2.

  12. Ari row-reduces the system in the figure to the last table [1, 2, -1 | 5; 0, 1, 3 | 12; 0, 0, 1 | 2]. What is x?

  13. Start

    [1, 3, 2 | 11; 2, 7, 2 | 15; 5, 16, 9 | 51]. Row steps: row 2 − 2 × row 1, then row 3 − 5 × row 1, then row 3 − row 2.

  14. Bo row-reduces the system in the figure to the last table [1, 3, 2 | 11; 0, 1, -2 | -7; 0, 0, 1 | 3]. 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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