Page 101 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
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Solution
The augmented matrix is
which can be reduced to row-echelon form as follows:
It is now evident from the third row in the matrix that the system has a solution if and only if , , and satisfy the condition
To express this condition another way, is consistent if and only if b is a matrix of the form
where and are arbitrary.
EXAMPLE 4 Determining Consistency by Elimination
What conditions must , , and satisfy in order for the system of equations
to be consistent?
Solution
The augmented matrix is
Reducing this to reduced row-echelon form yields (verify)
