Decide whether the following sets of vectors span the given vector space, are linearly independent or dependent, and form a basis for the given vector space: (a) ㅔ 0 -7 4 9 (b) «{[=]} (c) *{3-93) (No answer given) R³ (No answer given) R², (No answer given) R², is (No answer given) → is (No answer given) is (No answer given) ◆ and (No answer given) R³. and R². and R². (No answer given) (No answer given) ◆ for for ◆ for

a

7. Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x + 2, 2x + 3,−x² + x + 1} v=-3x² + 6x + 8 14 D b) B = {[1₁¹] [ = (₁ 3²1 -CAC) = B₂ -QAED = 0 v= c) B₁ v= 22

Express each of the following vectors in R² as linear combinations of the vectors [4] and (a) (b) (c) (d) 16 11 -36 17 -12 15 -20 = || = || - 4 Y + Y + -4 + Y + + + + A 4 -

3) Find a basis of F3 containing the vectors (1, 2, -3), (2, 6, -3)

Suppose V is a subspace of R" and suppose {v1, v2, v3} is a basis of V. Decide if the following sets of vectors are a basis for V: (i) {v2, v1 – 503, 2v3} (ii) {v2, v1 – 503, 203, 302 + 703 – v1} (iii) {202 – v3, v1}