solve a system with matrix inverses or augmented matrices

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

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

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

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

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

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

   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?

   5
5. 5.

   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?

   3
6. 6.

   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?

   -3

7. 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].

8. 7.

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

   5

9. Start

   [1, 3 | 13; 2, 8 | 36] (x + 3y = 13; 2x + 8y = 36). Row steps: row 2 − 2 × row 1 gives [0, 2 | 10]; then row 2 ÷ 2 gives [0, 1 | 5].

10. 8.

    Zee row-reduces the system in the figure and gets the last table [1, 3 | 13; 0, 1 | 5]. What is x?

    -2

11. Start

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

12. 9.

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

    6

13. 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].

14. 10.

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

    4