Is the statement "Two matrices are row equivalent if they have the same number of rows" true or false? Explain. A. True, because two matrices that are row equivalent have the same number of solutions, which means that they have the same number of rows. B. True, because two matrices are row equivalent if they have the same number of rows and column equivalent if they have the same number of columns. C. False, because if two matrices are row equivalent it means that there exists a sequence of row operations that transforms one matrix to the other. D. False, because if two matrices are row equivalent it means that they have the same number of row solutions.

Question

Zachariah Sullivan

Mathematics

25 November, 17:49

Is the statement "Two matrices are row equivalent if they have the same number of rows" true or false? Explain. A. True, because two matrices that are row equivalent have the same number of solutions, which means that they have the same number of rows. B. True, because two matrices are row equivalent if they have the same number of rows and column equivalent if they have the same number of columns. C. False, because if two matrices are row equivalent it means that there exists a sequence of row operations that transforms one matrix to the other. D. False, because if two matrices are row equivalent it means that they have the same number of row solutions.

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Louis Duke · Answer 1

Answer: The answer is (C).

Step-by-step explanation: The given statement is - "Two matrices are row equivalent if they have the same number of rows". We are to explain whether the statement is true or false.

What are row equivalent matrices? The answer to this question is -

Two matrices are said to be row equivalent if one of the matrices can be obtained from the other by applying a number of elementary row operations. Or, we can say two matrices of same order are row equivalent if they have same row space.

Thus, the correct option is (C).