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Solve the system using a matrix: -x - 7y - z = -19, 4y + 4z = 4, 2x + y + 6z = 7. What is the solution as an ordered triple (x, y, z)?

a) (-3, 2, 5)
b) (4, 0, 1)
c) (2, -3, 4)
d) (1, 5, -2)

User Parris
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1 Answer

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Final answer:

To solve the system of equations using matrices, rewrite the system as an augmented matrix, use row operations to simplify, and find the ordered triple that satisfies all the equations.

Step-by-step explanation:

To solve the system of equations using a matrix, we can write the system as an augmented matrix and then use row operations to reduce it to row-echelon form.

The system of equations is:

1) -x - 7y - z = -19

2) 4y + 4z = 4

3) 2x + y + 6z = 7

We can rewrite this system as an augmented matrix:

| -1 -7 -1 | -19 |

| 0 4 4 | 4 |

| 2 1 6 | 7 |

Next, we perform row operations to reduce the matrix into reduced row-echelon form:

R1 → R1

R2 → R2 / 4

R3 → R3 + 0.5 * R1

After simplifying, we should end up with a matrix that allows us to determine the values of x, y, and z directly.

The solution to the system will be an ordered triple of the form (x, y, z). The possible answers are given as options a) (-3, 2, 5), b) (4, 0, 1), c) (2, -3, 4), and d) (1, 5, -2).

After performing all the row operations correctly, we can find the correct ordered triple that satisfies all three equations in the system.

User Kessy
by
8.5k points
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