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Math 333 (2015) - Homework 1 Due: September 10, 2015. NAME: Most of the homework is a selection of exercises chosen from the textbook. Show your work in each problem. Staple this sheet to the front of your assignment 1) Section 1.1: #12 2) Section 1.2: #5 3) Section 1.3: #1 4) Section 1.4: #10 5) Section 1.4: #20 6) Section 1.4: #39 7) Section 1.4: #45 8) Section 1.4: #46 (Use the IRm×n notation) 9) Let A ∈ IR3×3 be given by 1 2 3 A= 1 4 1 2 1 8 Using standard Gaussian elimination A ∼ B where B is upper triangular with ones on the diagonal: 1 ∗ ∗ B= 0 1 ∗ 0 0 1 Here I do not mean reduced echelon form but rather echelon form with ones on the diagonal. Find elementary matrices Ei such that E3 E2 E1 A = B as demonstrated in class. E3 should be a diagonal scaling matrix.