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QUESTION 4 Show that ū€ span {(1,2,-1,0), (1,1,0,1),(0,0,1,1)} where ū= (0, -2,5,- 1) by finding scalars K, I and m such that ū=k(1,2,-1,0) + (1,1,0,1)+m(0,0,-1,1). k= m

QUESTION 4 Show that ū€ span {(1,2,-1,0), (1,1,0,1),(0,0,1,1)} where ū= (0, -2,5,- 1) by finding scalars K, I and m such that ū=k(1,2,-1,0) + (1,1,0,1)+m(0,0,-1,1). k= m

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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QUESTION 4 Show that uE span{(1,2, – 1,0),(1,1,0,1),(0,0, –1,1)} where u= (0, - 2,5, – 1) by finding scalars k,l and m such thatū = k(1,2, – 1,0) + I(1,1,0,1)+ m(0,0, – 1,1). k= m =
Transcribed Image Text:QUESTION 4 Show that uE span{(1,2, – 1,0),(1,1,0,1),(0,0, –1,1)} where u= (0, - 2,5, – 1) by finding scalars k,l and m such thatū = k(1,2, – 1,0) + I(1,1,0,1)+ m(0,0, – 1,1). k= m =
QUESTION 5 Determine whether the following is TRUE or FALSE: Let V be the set of all ordered pairs with the standard vector addition, but with scalar multiplication defined by k(x, y) = (kx,ky). This is not a vector space: for example, in general it is not the case that (k + Nu= ku+ lu for all u in V; and in particular, if k = 9, I=16 and u= (1,1) we obtain a counterexample. O True O False
Transcribed Image Text:QUESTION 5 Determine whether the following is TRUE or FALSE: Let V be the set of all ordered pairs with the standard vector addition, but with scalar multiplication defined by k(x, y) = (kx,ky). This is not a vector space: for example, in general it is not the case that (k + Nu= ku+ lu for all u in V; and in particular, if k = 9, I=16 and u= (1,1) we obtain a counterexample. O True O False
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