Schaum's Outline of Theory and Problems of Linear Algebra by Seymour Lipschutz

By Seymour Lipschutz

This booklet doesn't rather educate Linear Algebra. it's totally superficial and never attention-grabbing. try out Jim Hefferon's booklet as a substitute and you'll have a transparent textual content that teaches Linear Algebra for real.

Anyway, there are a number of workouts within the publication -- that's one cause to shop for it, I think...

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Extra info for Schaum's Outline of Theory and Problems of Linear Algebra (Schaum's Outlines)

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Ann bnn . P P Let AB ˆ ‰cij Š. Then cij ˆ nkˆ1 aik bkj and cii ˆ nkˆ1 aik bki . Suppose i > j. Then, for any k, either i > k or k > j, so that either aik ˆ 0 or bkj ˆ 0. Thus cij ˆ 0, and AB is upper triangular. Suppose i ˆ j. Then, for k < i, we have aik ˆ 0; and, for k > i, we have bki ˆ 0. Hence cii ˆ aii bii , as claimed. ] Lipschutz−Lipson:Schaum’s Outline of Theory and Problems of Linear Algebra, 3/e 2. Algebra of Matrices © The McGraw−Hill Companies, 2004 Text 50 ALGEBRA OF MATRICES [CHAP.

Compute AB using block multiplication, where 2 3 1 2 1 A ˆ 43 4 05 and 0 0 2  1 B ˆ 44 0 2 5 0 3 3 1 6 15 0 1    F R S and B ˆ , where E; F; G; R; S; T are the given blocks, and 01Â2 and 01Â3 T 01Â2 G are zero matrices of the indicated sites. 35. Let M ˆ diag…A; B; C†, where A ˆ 1 3   2 1 , B ˆ ‰5Š, C ˆ 4 5 Since M is block diagonal, square each block:   7 10 A2 ˆ ; B2 ˆ ‰25Š; 15 22 so C2 ˆ  16 40  24 ; 64 3 2 7 10 6 15 22 6 M2 ˆ 6 6 4  3 . Find M 2 . 36. Let f …x† and g…x† be polynomials and let A be a square matrix.

81. 1 63 6 Let U ˆ 4 0 0 2 4 0 0 0 0 5 3 0 0 1 4 3 2 3 3 À2 0 0 0 62 4 0 07 7 6 07 7 and V ˆ 6 0 0 1 27 7. 6 25 40 0 2 À3 5 1 0 0 À4 1 (a) Find UV using block multiplication. (c) Is UV block diagonal? 82. (b) Are U and V block diagonal matrices? Partition each of the following matrices so that it becomes a square block matrix with as many diagonal blocks as possible: 2 2 1 63 6 Bˆ6 60 40 0 3 1 0 0 A ˆ 4 0 0 2 5; 0 0 3 2 2 60 M ˆ6 40 0 0 1 2 0 0 4 1 0 2 0 0 0 0 3 0 07 7, (b) 05 3 0 0 4 5 0 0 0 0 0 0 3 0 07 7 07 7; 05 6 2 1 62 M ˆ6 40 0 2 0 C ˆ 40 2 1 3 0 0 0 0 1 4 3 1 0 0 05 0 0 3 0 07 7.

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