Worksheet

solve a system with matrix inverses or augmented matrices

Grade 11 Math Worksheet

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

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

    • [1, 2, -1; 3, -1, 0; 0, 2, 1][4; 5; 1] = [x; y; z]
    • [1, 2, -1; 3, -1, 0; 0, 2, 1][x; y; z] = [4; 5; 1]
    • [1, 2, -1; 3, -1, 0; 2, 1, 0][x; y; z] = [4; 5; 1]
    • [1, 3, 0; 2, -1, 2; -1, 0, 1][x; y; z] = [4; 5; 1]
    • [1, 2, 1; 3, -1, 0; 0, 2, 1][x; y; z] = [4; 5; 1]

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

    • [2, -1, 1; 1, 0, 4; 0, 1, -3][3; 2; 6] = [x; y; z]
    • [2, 1, 1; 1, 0, 4; 0, 1, -3][x; y; z] = [3; 2; 6]
    • [2, -1, 1; 1, 0, 4; 0, 1, -3][x; y; z] = [3; 2; 6]
    • [2, 1, 0; -1, 0, 1; 1, 4, -3][x; y; z] = [3; 2; 6]
    • [2, -1, 1; 1, 4, 0; 0, 1, -3][x; y; z] = [3; 2; 6]

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

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

  4. 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?

  5. 2x + 3y = 6; 4x + 9y = 6. Number table A = [2, 3; 4, 9]. Ren solves the system in the figure with X = A⁻¹B, where A⁻¹ = (1/6)[9, -3; -4, 2] and B = [6; 6]. What is y?

  6. 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?

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

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

  9. 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.

  10. 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?

  11. 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.

  12. 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?

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solve a system with matrix inverses or augmented matrices

Answer Key - Grade 11 Math Worksheet

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

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

    • [1, 2, -1; 3, -1, 0; 0, 2, 1][4; 5; 1] = [x; y; z]
    • [1, 2, -1; 3, -1, 0; 0, 2, 1][x; y; z] = [4; 5; 1]
    • [1, 2, -1; 3, -1, 0; 2, 1, 0][x; y; z] = [4; 5; 1]
    • [1, 3, 0; 2, -1, 2; -1, 0, 1][x; y; z] = [4; 5; 1]
    • [1, 2, 1; 3, -1, 0; 0, 2, 1][x; y; z] = [4; 5; 1]

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

    • [2, -1, 1; 1, 0, 4; 0, 1, -3][3; 2; 6] = [x; y; z]
    • [2, 1, 1; 1, 0, 4; 0, 1, -3][x; y; z] = [3; 2; 6]
    • [2, -1, 1; 1, 0, 4; 0, 1, -3][x; y; z] = [3; 2; 6]
    • [2, 1, 0; -1, 0, 1; 1, 4, -3][x; y; z] = [3; 2; 6]
    • [2, -1, 1; 1, 4, 0; 0, 1, -3][x; y; z] = [3; 2; 6]

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

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

  4. 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?

    6

  5. 2x + 3y = 6; 4x + 9y = 6. Number table A = [2, 3; 4, 9]. Ren solves the system in the figure with X = A⁻¹B, where A⁻¹ = (1/6)[9, -3; -4, 2] and B = [6; 6]. What is y?

    -2

  6. 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?

    -22

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

    7

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

    -1

  9. 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.

  10. 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?

    4

  11. 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.

  12. 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?

    -2