2 ai (How 1) Math-326 Define vector space And give at least One example? Q2. Consider v=R? then under usual addition and

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2 Ai How 1 Math 326 Define Vector Space And Give At Least One Example Q2 Consider V R Then Under Usual Addition And 1 (411.34 KiB) Viewed 25 times

2 ai (How 1) Math-326 Define vector space And give at least One example? Q2. Consider v=R? then under usual addition and scalas multiplication defined by: Ku =(x, ky for a scalar k and avector U=(ny) EV. (i) for u= (2,-4) and v = (1,-D - Compute Qu+3o. (11) show that U is not a vector space with given scalas multiplication Q3? - Decide which of the following subset are Subspace of R3. (a) W, = {(9,b,c); c=a+b3 (b) W2 = { (a, b, 1); a, bER? (C) W3 = {(a, b, o); ab ER}

(d) wu = { [a b]; a, b, c ER} = Maks(R) و с Scanned with CamScanner 2 e vector w=C1, -2,K) Qui for what value of K in R3 be a linear combination of vectors, u=(3,0,-2) and o=(2,-1,-5) a , Osi Decide which of the following setsale linecely independent in the vectos spacer? @ S,= {(1, 2, 1), (2, 1, 1), (8,1,1)} 1,2,4,-1( s={(1,2,-), (2,0,33 Q6? Decide which of the following sets are linearly independent in the vectos space P₂ (2) @ 8,-{ 2+2, 1-2, *+*?] ① S2 ={ 143 8+242, 34x + 2x², 2x + x² 3. 3xx *+?} 1+ 2