MAT223H1 Lecture Notes - Lecture 5: Coefficient Matrix, Row Echelon Form, Free Variables And Bound Variables
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Example 1. 4 (on the reduction algorithm: black is called the constant matrix (a, red is called the coefficient matrix (b) Step 1: select the left-most non-zero column (which is the column with 0, 2, 4) [(cid:882) (cid:883) (cid:888) (cid:885) (cid:886) (cid:883) (cid:882) (cid:883)] [(cid:1827)|(cid:1854)] (cid:884) (cid:884) (cid:884) (cid:886) [(cid:882) (cid:883) (cid:888) (cid:885) (cid:886) (cid:883) (cid:882) (cid:883)] (cid:884) (cid:884) (cid:884) (cid:886) [(cid:884) (cid:884) (cid:886) (cid:884) (cid:882) (cid:885) (cid:886) (cid:889)] (cid:882) (cid:883) (cid:885) (cid:888) Step 2: select non-zero entry of column and move it into the pivot position by interchanging the rows. No(cid:449) (cid:449)e"(cid:448)e produ(cid:272)ed all the (cid:374)o(cid:374)-zero terms to zeros. Step 4: cover the first row and repeat (steps 1 to 3) to the resulting submatrix. End result: we first obtain: then perform the backwards algorithm. [(cid:884) (cid:884) (cid:884) (cid:886) (cid:886) (cid:883) (cid:882) (cid:883)] (cid:882) (cid:883) (cid:888) (cid:885) [(cid:884) (cid:882) (cid:882) (cid:883)(cid:886) ] (cid:882) (cid:883) [(cid:883) (cid:882) (cid:884) (cid:884) (cid:882) (cid:883) 9 (cid:884)]
