Answered: 2x3 1. Consider the inner product space… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 94E

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2x3
1. Consider the inner product space (R2×³, (.,-)), where
2 3
(A, B)=ajbij, VA, B € R2×3
i=1 j=1
Let
and define the set
C =
1 2 0
000
8), D = (8
= (8 33 1),
0 0
S = {A € R2×3 | A is orthogonal to both C and D},
which can be shown to be a subspace of R2×3. Find a basis for S.

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4. Consider -- -- *-H = = V3-1 2 k a) For what values of k is v3 in Span {V₁, V₂}? Explain. b) For what values of k is {v₁, v2, V3} linearly dependent? Explain. [-51 6 0
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