SOLUTION: Help Needed; Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent. x - y + 3z = 11

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Question 201959: Help Needed;
Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent.
x - y + 3z = 11
4x + z = 2
x + 3y + z = -13
A) Dependent
B) Inconsistent
C) Independent
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, construct the augmented matrix by writing the coefficients and right hand constants:

+%28matrix%283%2C4%2C1%2C-1%2C11%2C4%2C0%2C1%2C2%2C1%2C3%2C1%2C-13%29%29+


Now let's perform row reductions to determine whether the system is independent, dependent, or inconsistent (solution provided by the Linear Algebra Toolkit)







From the last matrix, we can see that there is a value of 1 in every pivot position. So this means that there is a unique solution, which means that the system is independent.


So the answer is C) Independent