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Chapter 1 Section 2

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Example 1: R1+R2 R2 2R1+R3 R3 R5-R1 R5

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Example 1: R1+R2 R2 2R1+R3 R3 R5-R1 R5 A system is said to be in strict triangular form if, in the kth equation, the coefficients of the first k-1 variables are all zero and the coefficients of the x k is nonzero (k=1,…,n)

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Example 1: R3-2R2 R3 R4-R2 R4 R5-R2 R5

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Example 1: R4-R3 R4 R3-R5 R5

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Example 2: R1+R2 R2 2R1+R3 R3 R5-R1 R5

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Example 2: R3-2R2 R3 R4-R2 R4 R4-R3 R4 R5-R4 R5

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Which matrices are in Row Echelon form? No Violates Rule 1 Yes No Violates Rule 3 No Violates Rule 2 Yes

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Example 4: System A R1-R2 R2 ½R2 R2 R1+R3 R3 3R2-R3 R3 -½ R3 R3

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Example 4: System B 2R1-R2 R2 4R1-R3 R3 2R1-R4 R4 R2-R3 R3 R3 R4

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Example 4: System B R2-R3 R3 ⅕ R2 R2 ½R3 R3

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Example 4: System C 2R1-R2 R2 4R1-R3 R3 R2-R3 R3 R3 R4 3R1-R3 R3

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Example 4: System C R2-R3 R3 ⅕ R2 R1

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Example 5: System A 2R1-R2 R2 -R2 R2

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Example 5: System B R2-R1 R2 R3-R1 R3 R3-R2 R3 R2-R3 R2 R1-R3 R1 R1-R2 R1

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4.6: Rank. Definition: Let A be an mxn matrix. Then each row of A has n entries and can therefore be associated with a vector in The set of all linear.

4.6: Rank. Definition: Let A be an mxn matrix. Then each row of A has n entries and can therefore be associated with a vector in The set of all linear.

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