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. 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; 2, 1, 0][x; y; z] = [4; 5; 1]
   • [1, 2, 1; 3, -1, 0; 0, 2, 1][x; y; z] = [4; 5; 1]
   • [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, 3, 0; 2, -1, 2; -1, 0, 1][x; y; z] = [4; 5; 1]
2. 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][x; y; z] = [3; 2; 6]
   • [2, -1, 1; 1, 4, 0; 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, 0, 4; 0, 1, -3][x; y; z] = [3; 2; 6]
   • [2, -1, 1; 1, 0, 4; 0, 1, -3][3; 2; 6] = [x; y; z]
3. 3.

   5x + 2y = -7; 7x + 3y = -9. Number table A = [5, 2; 7, 3]. Noah solves the system in the figure with X = A⁻¹B, where A⁻¹ = [3, -2; -7, 5] and B = [-7; -9]. What is y?

   4
4. 4.

   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
5. 5.

   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
6. 6.

   Kira replaces row 2 of [1, -2 | 3; 5, 2 | 9] with row 2 − 5 × row 1. What is the new number in row 2, after the bar?

   -6
7. 7.

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

   4

8. 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.

9. 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?

   4

10. 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.

11. 9.

    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

12. 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.

13. 10.

    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?

    -5