Question

Maggie is solving the system of three linear equations in three variables using matrices.

2x + y - 3z = -10
3x - y + 2z = 17
2x + 4y + 6z = 2
If Maggie solves the system of three equations in three unknowns using matrices, which of the matrices would best represent her answer?

A) [2, 1, -3; 3, -1, 2; 2, 4, 6]
B) [2, 3, 2; 1, -1, 4; -3, 2, 6]
C) [2, 3, 2; 1, -1, 4; -10, 17, 2]
D) [3, 2, 2; 4, -1, 3; -10, 17, 2]

Answer 1

Maggie is solving the system of three linear equations using matrices, and the correct matrix representation of her system is an augmented matrix [2, 3, 2; 1, -1, 4; -10, 17, 2], which includes the coefficients of variables and constant terms.

Step-by-step explanation:

Maggie is solving the system of three linear equations in three variables using matrices. The system given is:

• 2x + y - 3z = -10
• 3x - y + 2z = 17
• 2x + 4y + 6z = 2

When these equations are transformed into matrix form, they are represented by the coefficient matrix and the constants on the right side of each equation. The proper matrix includes both the coefficients of the variables x, y, and z and the constant terms from each equation in one combined matrix, known as the augmented matrix.

Therefore, the correct matrix that would best represent her answer is:

C) [2, 3, 2; 1, -1, 4; -10, 17, 2]

This augmented matrix correctly lines up the coefficients from each equation and their corresponding constant terms on the right-hand side.