Representation a System of Linear

For the system 2x + 3y = 7 and -x + 4y = 5, the coefficient matrix A is:

• [[2, 3], [-1, 4]]

• [[2, -1], [3, 4]]

• [[7, 5], [2, 3]]

• [[2, 3], [7, 5]]

Tags

CCSS.HSA.REI.C.8

For the same system, the variable matrix X is:

• [x, y]

• [x; y] (a column vector)

• [7; 5]

• [2; -1]

For the same system, the constant matrix B is:

• [2; 3]

• [x; y]

• [7; 5]

• [-1; 4]

Tags

CCSS.HSN.VM.C.6

Which matrix equation represents x - 2y + 3z = 4 and 2x + y - z = 0 ?

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

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

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

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

Tags

CCSS.HSA.REI.C.8

Which augmented matrix [A | B] correctly represents 3x + 2y = 8 and 5x - y = 1 ?

• [[3, 2 | 8], [5, -1 | 1]]

• [[3, 2 | 5], [8, -1 | 1]]

• [[8, 3 | 2], [1, 5 | -1]]

• [[3, 5 | 8], [2, -1 | 1]]

Tags

CCSS.HSA.REI.C.8

A system has 4 equations and 3 unknowns. The size of A is:

• 4 x 3

• 3 x 4

• 3 x 3

• 4 x 4

Tags

CCSS.HSA.REI.C.8

For a system with 3 equations in 2 variables, which sizes make AX = B valid?

• A: 2x3, X: 3x1, B: 2x1

• A: 3x2, X: 2x1, B: 3x1

• A: 3x3, X: 2x1, B: 3x1

• A: 2x2, X: 3x1, B: 2x1

Given A = [[1, 3], [2, -1]], X = [x; y], B = [5; 0]. Which system matches AX = B?

• x + 3y = 5, 2x - y = 0

• x + 2y = 5, 3x - y = 0

• x + 3y = 0, 2x - y = 5

• x - 3y = 5, 2x + y = 0

Tags

CCSS.HSA.REI.C.8

Write AX = B with X = [x; y] for 4y - x = 6 and y + 2x = 3. The correct A and B are:

• A = [[4, -1], [1, 2]], B = [6; 3]

• A = [[-1, 4], [2, 1]], B = [6; 3]

• A = [[-1, 4], [1, 2]], B = [3; 6]

• A = [[1, -4], [2, 1]], B = [6; 3]

Tags

CCSS.HSA.REI.C.8

Is AX = B well-defined if A is 2x2, X is 3x1, and B is 2x1?

• Yes, dimensions match.

• No, A and X are incompatible.

• Yes, because B is 2x1.

• No, because B must be 3x1.

Tags

CCSS.HSN.VM.C.8