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# sol1 - Mathematics 20F Fall 2008 Quiz 1 Name No aids are...

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Mathematics 20F Fall 2008 Name: Quiz 1 No aids are allowed. Be sure to write down all row operations used. 1) (5 points) Using elementary row operations, row reduce the following matrix into Reduced Row Echelon Form : 1 2 1 1 2 4 0 - 2 - 2 - 4 - 2 1 . Then, answer the following question: if the above matrix is the augmented matrix for some linear system, is the system consistant?

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1 2 1 1 2 4 0 - 2 - 2 - 4 - 2 1 R 2 R 2 - 2 R 1 -------→ 1 2 1 1 0 0 - 2 - 4 - 2 - 4 - 2 1 R 3 R 3 +2 R 1 -------→ 1 2 1 1 0 0 - 2 - 4 0 0 0 3 R 3 1 3 R 3 -----→ 1 2 1 1 0 0 - 2 - 4 0 0 0 1 R 2 R 2 +4 R 3 -------→ 1 2 1 1 0 0 - 2 0 0 0 0 1 R 1 R 1 - R 3 -------→ 1 2 1 0 0 0 - 2 0 0 0 0 1 R 2 ←- 1 2 R 2 ------→ 1 2 1 0 0 0 1 0 0 0 0 1 R 1 R 1 - R 2 -------→ 1 2 0 0 0 0 1 0 0 0 0 1 If this is the augmented matrix for some linear system, then the last row describes the equation 0 = 1 and hence this system is inconsistent.

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sol1 - Mathematics 20F Fall 2008 Quiz 1 Name No aids are...

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