Question

I need 6(d),7(a) (b) (c) (d). Thank you

(a) the NSA 16) (5 ) F o r the RSA SA (d) (5 ) etc) formo CSA) has this w o rth with the RExplain 7. Determine whether each wat is either trofale. If we give justification known fact if Cae, give a comer example (a) (4 points) 2. are vectors of a subpace W of R", then so are all vectors of Span(2.57 (b) (points) de A)=0 then A (c) (points) Suppose A is an e x matrix. If det(A) , the Rank(A) < in the interval ( b). (d) points) If the Wronki W then the function a l r ) for women ly dependent on that interval

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Answer 1

Son & Tone ², Y E W . W subspae or IRM. » añ I B y Ew for any scalar (because w is a &ß. a subspace) Span {x, Ý } cwe w Note: Span{ ,83=La X + B r l xiß are scalars} 6 false Let A=[!!], det (AD= 1.1-111=0 but A mass does not have any zero row True Rank(A), = ' Larsent submatrix of Sot determinant or submatrix is N0+ е и с to 2ето Here det (A)= o so larsest submarix must be rxx where ran - Rank (A)=r an @ False To be linearly dependent it should be zero * for all necaib) (a,b) ex: let fox x², g(x)=1 on (5.5) w= w I fe 22 11 22 11 =x-2x I d x² di 2x ol It d

W = 0 = 2²-2x = 0 = x²(x-2) = 0 = x=0, x-2=0 = x=2 Here w (f(xo), g(xo) 20 for EC-510 no=2 & noso but not dependent on f &g are (5-5,5) its 2x2+ßx=0 = x=B=0 ) x²&1 are independent 6 @ Basis for CS B S To form Basis for IR3 we need 3 linearly Independent vectors in IR? two we already have 2 vecters Dand any vector a which is not in CS (A) Dis Independent to CSA) So & Any one vectors from outsise cs (A) & Basis for cŚ(A) will form Dasis for RRSC Any vecter Not in cS (A) will work? For example criz5-31 I 2 1 - 2 DVOJZ 4 LII I is a basis for IR3