1. Consider the set of vectors: '8 w= {M, = 6 ), M2 = (; ), M3 = (8 ),M. = ( )}< M2x2 (R). W = (a) The vector M = -10 G 0) belongs to the vector subspace generated by W, [W]? Justify! (b) Determine the vector subspace of M2x2 (IR) generated by W, [W]. (c) Determine a basis ßc {W1, W2, Ws, W4} for the subspace [W].

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Consider the set of vectors:
'8
w= {M, = 6 ), M2 = (; ), M3 = (8 ),M. = ( )}< M2x2 (R).
W =
-10
(a) The vector M =
G ) belongs to the vector subspace generated by Ww, [W]?
Justify!
(b) Determine the vector subspace of M2x2 (IR) generated by W, [W].
(c) Determine a basis ßc {W1, W2, Ws, W4} for the subspace [W].
Transcribed Image Text:1. Consider the set of vectors: '8 w= {M, = 6 ), M2 = (; ), M3 = (8 ),M. = ( )}< M2x2 (R). W = -10 (a) The vector M = G ) belongs to the vector subspace generated by Ww, [W]? Justify! (b) Determine the vector subspace of M2x2 (IR) generated by W, [W]. (c) Determine a basis ßc {W1, W2, Ws, W4} for the subspace [W].
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