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Linear Algebra

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Solution to System in Row Echelon Form

LINALG-KSQP7Y

Suppose that a linear system in four variables can be represented by an augmented matrix $M$. Further suppose that the reduced row echelon form of $M$ is the matrix given below. Which of the following $4$-tuples represents a solution to the system? There may be more than one correct answer. Choose all correct answers.

$$M=\left [\matrix {1 & 1 & 1 & 1& 1 \cr 0 & 0 & 1 & 1& 1 \cr 0 & 0& 0 & 1 & 1\cr 0 & 0 & 0 & 0 & 0\cr }\right ]$$

A

$(1, 1, 1, 1)$

B

$(1, 1, 1, 0)$

C

$(1, -1, 0, 1)$

D

$(-2, 2, 0, 1)$

E

$(1, 1, -1, 1)$

F

$(1,1, 0, 0)$

G

$(0, 0, 0, 1)$

H

None of the above.