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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 - Building Confidence

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  1. Luz writes the system 2x + 3y = 7 and 5x − y = 4 as AX = B. Which matrix equation is it?

    • [2, 3; 5, 1][x; y] = [7; 4]
    • [2, 5; 3, -1][x; y] = [7; 4]
    • [2, 3; 5, -1][x; y] = [7; 4]
    • [2, 3; 5, -1][7; 4] = [x; y]

  2. Milo writes the system 4x − 3y = 2 and x + 2y = 6 as AX = B. Which matrix equation is it?

    • [4, -3; 1, 2][2; 6] = [x; y]
    • [4, 1; -3, 2][x; y] = [2; 6]
    • [4, 3; 1, 2][x; y] = [2; 6]
    • [4, -3; 1, 2][x; y] = [2; 6]

  3. Noah writes the system 3x + y = 9 and 2x − 5y = 1 as AX = B. Which matrix equation is it?

    • [3, 1; 2, 5][x; y] = [9; 1]
    • [3, 2; 1, -5][x; y] = [9; 1]
    • [3, 1; 2, -5][9; 1] = [x; y]
    • [3, 1; 2, -5][x; y] = [9; 1]

  4. Pia writes the system 6x − y = 5 and 3x − 2y = 4 as AX = B. Which matrix equation is it?

    • [6, 3; -1, -2][x; y] = [5; 4]
    • [6, -1; 3, -2][5; 4] = [x; y]
    • [6, -1; 3, -2][x; y] = [5; 4]
    • [6, 1; 3, -2][x; y] = [5; 4]

  5. 3x + 2y = 11; 4x + 3y = 14. Number table A = [3, 2; 4, 3]. Jun solves the system in the figure with X = A⁻¹B, where A⁻¹ = [3, -2; -4, 3] and B = [11; 14]. What is x?

  6. 2x + y = 4; 4x + 5y = 2. Number table A = [2, 1; 4, 5]. Luz solves the system in the figure with X = A⁻¹B, where A⁻¹ = (1/6)[5, -1; -4, 2] and B = [4; 2]. What is x?

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

  8. Read this first

    Start

    [1, 2 | 11; 4, 9 | 47] (x + 2y = 11; 4x + 9y = 47). Row steps: row 2 − 4 × row 1 gives [0, 1 | 3].

  9. Tala row-reduces the system in the figure and gets the last table [1, 2 | 11; 0, 1 | 3]. What is x?

  10. Start

    [1, 5 | 16; 2, 11 | 34] (x + 5y = 16; 2x + 11y = 34). Row steps: row 2 − 2 × row 1 gives [0, 1 | 2].

  11. Ari row-reduces the system in the figure and gets the last table [1, 5 | 16; 0, 1 | 2]. What is x?

  12. Start

    [1, -2 | -10; 2, 1 | 15] (x − 2y = -10; 2x + y = 15). Row steps: row 2 − 2 × row 1 gives [0, 5 | 35]; then row 2 ÷ 5 gives [0, 1 | 7].

  13. Bo row-reduces the system in the figure and gets the last table [1, -2 | -10; 0, 1 | 7]. 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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