(4) Circle the correct answer or fill in the blanks. (You do not have to give...

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(4) Circle the correct answer or fill in the blanks. (You do not have to give explanations.) (a) Is set of vectors (8,2 sin²r, 4 cos²x} linearly independent? Circle YES or NO. (b) Is W is a subspace of R³ if W = {(£): SER}" a,bER Circle YES or NO. If W is a subspace, the dimension of W is and a basis for W is. (c) Is W is a subspace of R³ if W = {(E) b Circle YES or NO. If W is a subspace, the dimension of W is and a basis for W is (d) Let V denote the vector space of all 2 x 2 matrices over R, and let W be the set of all matrices (an a12) 021 022) with a12=3021. Is W a subspace of V? Circle YES or NO. A = : a,b ER? If W is a subspace, the dimension of W is and a basis for W is (e) Consider the vector subspace W = {(a, b, c, d, e) ER: a=0, 2b-d=0} (i) The dimension of W is (ii) A basis for W is (f) The dimension of the vector space of all 2 x 2 upper triangular matrices over IR is (g) A basis for of the vector space of all 2 x 2 upper triangular matrices over R is (h) Is in the span of S= - {(₁)-(-²)}² ? Circle YES or NO. (4) Circle the correct answer or fill in the blanks. (You do not have to give explanations.) (a) Is set of vectors (8,2 sin²r, 4 cos²x} linearly independent? Circle YES or NO. (b) Is W is a subspace of R³ if W = {(£): SER}" a,bER Circle YES or NO. If W is a subspace, the dimension of W is and a basis for W is. (c) Is W is a subspace of R³ if W = {(E) b Circle YES or NO. If W is a subspace, the dimension of W is and a basis for W is (d) Let V denote the vector space of all 2 x 2 matrices over R, and let W be the set of all matrices (an a12) 021 022) with a12=3021. Is W a subspace of V? Circle YES or NO. A = : a,b ER? If W is a subspace, the dimension of W is and a basis for W is (e) Consider the vector subspace W = {(a, b, c, d, e) ER: a=0, 2b-d=0} (i) The dimension of W is (ii) A basis for W is (f) The dimension of the vector space of all 2 x 2 upper triangular matrices over IR is (g) A basis for of the vector space of all 2 x 2 upper triangular matrices over R is (h) Is in the span of S= - {(₁)-(-²)}² ? Circle YES or NO.