Write the linear system corresponding to the reduced augmented matrix.
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A) x1 = -4, x2 = t + 6, x3 = t for any real number t
B) x1 = 4, x2 = t + 6, x3 = 0
C) No Solution
D) x1 = 4, x2 = -t + 6, x3 = t for any real number t

Question

Write the linear system corresponding to the reduced augmented matrix.
-
A) x1 = -4, x2 = t + 6, x3 = t for any real number t 
B) x1 = 4, x2 = t + 6, x3 = 0 
C) No Solution 
D) x1 = 4, x2 = -t + 6, x3 = t for any real number t

Quizplus · Accepted Answer

The reduced augmented matrix can be written as:
|1 0 0  |  4  |
|0 1 -1 |  6  |
|0 0 0  |  t  |

This corresponds to the system of equations:

x1 = 4
x2 - x3 = 6
0 = t

Solving the third equation, we get t = 0. Substituting this value in the second equation, we get x2 - x3 = 6, which can be written as x2 = t + 6 and x3 = -t. Substituting these values in the first equation, we get x1 = 4.

Therefore, the solution to the system of equations is x1 = 4, x2 = -t + 6, x3 = t, for any real number t.

Hence, the correct choice is D. The reduced augmented matrix is in the form:

1 0 t+2 | 4
0 1 -t+4 | 6
0 0 0 | 0

From this, we can see that:

x1 = 4
x2 = -t+6
x3 = t

Therefore, the solution is given by choice D.

Write the Linear System Corresponding to the Reduced Augmented Matrix