104 - augmented matrix = 6 − 3 = 3. a redundant equation...

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1 Gaussian elimination: an algorithm for finding a (actually “the”) reduced row echelon form of a matrix. pivot position pivot column previous [ A b ] interchange rows 1 and 2 pivot position pivot column
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2 pivot position pivot column multiply row 3 by 1/2 : a row echelon form add ( 3) × (row 3) to row 1 add 5 × (row 3) to row 2 multiply row 2 by 1/2 add row 2 to row 1 the reduced row echelon form steps 1-4: forward pass a row echelon form steps 5-6: backward pass a reduced row echelon form
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3 Example end of forward pass, a row echelon form general solution: In the above example, rank of the augmented matrix = 3, and nullity of the
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Unformatted text preview: augmented matrix = 6 − 3 = 3. a redundant equation is eliminated to become 0 = 0 4 Proof (a) ⇔ (b): (b) means ∃ v = [ v 1 v 2 " v n ] T such that A v = [ a 1 a 2 " a n ] v = v 1 a 1 + v 2 a 2 + " + v n a n = b thus v is a solution, and A x = b is consistent. 5 * (a) ⇔ (c): Explained in Section 1.3. (a) ⇔ (d): Let [ R c ] be the reduced row echelon form of [ A b ], then from the definition of the reduced echelon form, R is the reduced row echelon form of A . (d) means that no nonzero entries of c appear at zero rows of R , which is exactly what (c) means....
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104 - augmented matrix = 6 − 3 = 3. a redundant equation...

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