Mark each statement True or False (T/F). Justify each answer. (If true, cite appropriate facts or theorems. If false, explain why or give a counterexample that shows why the statement is not true in every case.
1. (T/F) Every matrix is row equivalent to a unique matrix in echelon form.
To decide: if the given statement is true or false.
Answer to Problem 1SE
False.
Explanation of Solution
Given information:
The statement, “Every matrix is row equivalent to a unique matrix in echelon form.”
Theorem Used:
Uniqueness of the Reduced Echelon Form:
Each matrix is row equivalent to one and only one reduced echelon matrix.
The given statement is false.
By the above theorem it is clear that every matrix is row equivalent to a unique matrix in only reduced echelon form and not the echelon form.
Hence, the statement is false.
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