Q-3: a) Let W%3D ((а + с, а +b+2с, а + с,а - b) :а,b, с €R}. i. Show that W is a subspace of R. ii. Find a basis for W. , Find a basis of R* that contains the vectors X = (1, 1, 1, 1) and Y = (1, 1,0, 1).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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B7
Q-3:
a)
W = {(a +c, a +b+ 2c, a + c, a – b):a, b,c e R}.
i. Show that W is a subspace of R.
ii. Find a basis for W.
Let
Find a basis of R* that contains the vectors
b)
X = (1, 1, 1, 1) and Y = (1, 1,0, 1).
Transcribed Image Text:Q-3: a) W = {(a +c, a +b+ 2c, a + c, a – b):a, b,c e R}. i. Show that W is a subspace of R. ii. Find a basis for W. Let Find a basis of R* that contains the vectors b) X = (1, 1, 1, 1) and Y = (1, 1,0, 1).
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