solve a system with matrix inverses or augmented matrices
Grade 11 Math Worksheet
Circle the best answer, or write your answer on the line.
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; 0, 2, 1][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; 2, 1, 0][x; y; z] = [4; 5; 1]
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]
- [3, 2; 1, -4][x; y] = [8; 1]
- [2, 3; 1, -4][8; 1] = [x; y]
Esme writes the system 5x − 2y = 3 and 4y + x = 9 as AX = B. Which matrix equation is it?
- [5, 1; -2, 4][x; y] = [3; 9]
- [5, -2; 1, 4][3; 9] = [x; y]
- [5, -2; 1, 4][x; y] = [3; 9]
- [5, -2; 4, 1][x; y] = [3; 9]
- [5, 2; 1, 4][x; y] = [3; 9]
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?
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?
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?
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?
Ren solves 3x + 4y = 5 and 2x + 5y = 8 with X = A⁻¹B. What is x?
Tala solves 4x + y = 5 and 3x + 2y = 0 with X = A⁻¹B. What is y?
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[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.
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?