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Solutions to Homework Assignment 1_2

# Solutions to Homework Assignment 1_2 - Solutions to...

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Solutions to Homework Section 1.2 #1, 3, 7, 11, 13, 17, 19, 21 1. Study Guide: To check whether a matrix is in echelon form, ask these questions: (i). Is every nonzero row above the all-zero rows (if any)? Matrix (c) fails this test, so it is NOT in echelon form. (ii). Are the leading entries in a stair-step pattern, with zeros below each leading entry? Matrices (a), (b), and (d) all pass tests (i) and (ii), so they are in echelon form. Now check to see if they are actually in reduced echelon form… To check whether a matrix in echelon form is actually in reduced echelon form, ask two more questions: (iii). Is there a 1 in every pivot position? Matrix (d) fails this test, so it is only in echelon form. Finally, ask: (iv). Does each leading 1 have all zeros above it (and below it)? Matrices (a) and (b) pass all four tests, so they are in reduced echelon form. 3. This final matrix is in reduced echelon form and the pivot positions are circled. Original matrix: The pivot columns are 1 and 3.

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