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Explain the error in the following argument claiming that any matrix with at least two rows is row-equivalent to a matrix with a zero row: "Perform R1 – R2 and R2 – R (in alternate notation, these would be R1 : RỊ – R2 and R2: R2 – R1). Then row 1 is -1 times row 2. Now, perform R2 + R to obtain a row of zeroes in the second row."

Explain the error in the following argument claiming that any matrix with at least two rows is row-equivalent to a matrix with a zero row: "Perform R1 – R2 and R2 – R (in alternate notation, these would be R1 : RỊ – R2 and R2: R2 – R1). Then row 1 is -1 times row 2. Now, perform R2 + R to obtain a row of zeroes in the second row."

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Explain the error in the following argument claiming that any matrix with at least two rows is row-equivalent to a matrix with a zero row: "Perform R1 – R2 and R2 – Rị (in alternate notation, these would be R1 : R1 – R2 and R2 : R2 – R1). Then row 1 is -1 times row 2. Now, perform R2 + R to obtain a row of zeroes in the second row."
Transcribed Image Text:Explain the error in the following argument claiming that any matrix with at least two rows is row-equivalent to a matrix with a zero row: "Perform R1 – R2 and R2 – Rị (in alternate notation, these would be R1 : R1 – R2 and R2 : R2 – R1). Then row 1 is -1 times row 2. Now, perform R2 + R to obtain a row of zeroes in the second row."
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