1.6 - Section 1.6 Transforming a matrix to Reduced Echelon...

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Section 1.6 Transforming a matrix to Reduced Echelon Form The size of a matrix is mXn where m is the number of rows and n is the number of columns. Example: 123 456 789 10 11 12 13 14 15 is a 5 X 3 matrix. Theorem: Let A be a mXn matrix (m rows and n columns). There is a unique reduced echelon mXn matrix B such that A can be transformed to B by a series of elementary row operations i.e. any matrix can be transformed to a unique reduced echelon matrix.
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Example : Use elementary row operations to get to reduced echelon form. 000 05 7 9 012 1 0 1 0 12 3 0 047   −−  : Solution 13 R R 12 3 0 047 1 0 1 0 7 9 1 R 1 2 300 4 7 1 01 0 000057 9 2 RR + 107 20 2 7 10 1 0 0 5 7 9 3 1 5 R 2 7 1 0 79 0 1 55 Note: 4 steps
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Example : There are three numbers whose sum is 34. The sum of the first and second is 7 and the sum of the second and third is 22. Find the numbers. 123
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1.6 - Section 1.6 Transforming a matrix to Reduced Echelon...

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