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M21001-HW2

# M21001-HW2 - MATH 21001 Spring 2010 Homework 2 Hassan...

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MATH 21001 - Spring 2010 - Homework 2 Hassan Allouba Problem 1 Reduce each of the following matrices to row echelon form, determine the rank, and identify the basic columns. ( a ) 1 2 3 3 2 4 6 9 2 6 7 6 ( b ) 1 2 3 2 6 8 2 6 0 1 2 5 3 8 6 ( c ) 2 1 1 3 0 4 1 4 2 4 4 1 5 5 2 1 3 1 0 4 3 6 3 4 8 1 9 5 0 0 3 - 3 0 0 3 8 4 2 14 1 13 3 Problem 2 How many different “forms” are possible for a 3 × 4 matrix that is in row echelon form? Problem 3 Suppose that [ A | b ] is reduced to a matrix [ E | c ]. (a) Is [ E | c ] in row echelon form if E is? (b) If [ E | c ] is in row echelon form, must E be in row echelon form? Problem 4 Determine the reduced row echelon form for each of the following matrices and then express each nonbasic column in terms of the basic columns: ( a ) 1 2 3 3 2 4 6 9 2 6 7 6 , ( b ) 2 1 1 3 0 4 1 4 2 4 4 1 5 5 2 1 3 1 0 4 3 6 3 4 8 1 9 5 0 0 3 - 3 0 0 3 8 4 2 14 1 13 3 . 1

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Problem 5 Construct a matrix A whose reduced row echelon form is E A = 1 2 0 - 3 0 0 0 0 0 1 - 4 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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