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Solved: The augmented matrices that follow are in row echelon form. For each case
Chapter 1, Problem 2(choose chapter or problem)
The augmented matrices that follow are in row echelon form. For each case, indicate whether the corresponding linear system is consistent. If the system has a unique solution, find it. (a) 1 2 4 0 1 3 0 0 1 (b) 1 3 1 0 1 1 0 0 0 (c) 1 2 4 1 001 3 000 0 (d) 1 2 2 2 0 1 1 3 001 2 (e) 132 2 001 4 000 1 (f)1 1 3 8012 7001 2000 0
Questions & Answers
QUESTION:
The augmented matrices that follow are in row echelon form. For each case, indicate whether the corresponding linear system is consistent. If the system has a unique solution, find it. (a) 1 2 4 0 1 3 0 0 1 (b) 1 3 1 0 1 1 0 0 0 (c) 1 2 4 1 001 3 000 0 (d) 1 2 2 2 0 1 1 3 001 2 (e) 132 2 001 4 000 1 (f)1 1 3 8012 7001 2000 0
ANSWER:Step 1 of 25
A unique solution exists for a set of linear simultaneous equations if and only if
The number of unknowns and equations are equal,
All equations are consistent.
No linear dependency exists between any two or more equations, i.e., all equations are independent.