HW 3 - MATH 225 HOMEWORK 3 pp. 159 161 #11 14, 22, 23, 40,...

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MATH 225 HOMEWORK 3 pp. 159 – 161 #11 – 14, 22, 23, 40, 41, 52 (In all cases identify a specific solution and the general solution of the corresponding homogeneous system.) pp. 170 – 171 8, 14 – 16, 23 – 25, 29, 31, 35, 36 A. Describe the solutions of the systems represented by the following augmented matrices [ AB ] and describe the general solution of the corresponding homogeneous system: i) 1 0 ! 1 2 1 0 1 1 1 0 0 0 0 0 0 " # $ $ % ' ' ii) 1 1 0 ! 1 0 1 0 0 1 1 0 2 0 0 0 0 1 3 " # $ $ % ' ' iii) 1 1 1 ! ! 1 1 0 1 1 ! ! 1 0 0 0 1 ! ! 1 1 0 0 0 1 ! 1 0 " " " " " " " 0 ! ! 0 1 1 0 0 0 0 ! 0 1 1 " # $ $ $ $ $ $ % ' ' ' ' ' ' R 11x12 ( A is the matrix with all entries on or above the diagonal equal to1 and all 0's below it, and B R 11 alternates its entries between 1 and 0: A i 12 = (–1) i +1 . B. Let A = " 2 3 3 0 1 1 0 " 3 " 2 1 2 3 0 1 1 " 2 # $ % % % ' ( ( ( M 4 ( R ). What homogeneous system of linear equations describes all B R 4 satisfying AB = B ? Describe all such B . How many free variables are there in the solution?
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HW 3 - MATH 225 HOMEWORK 3 pp. 159 161 #11 14, 22, 23, 40,...

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