Let v₁ = O 1 5, V₂ = No Yes -2 -7 13 and w= - 3 -6 19 Is w is in the subspace of R³ generated by v₁ and v₂? Determine if w is in the subspace of R³ generated by V, and v₂.

1 2 7 Let v, = and w = - 1 3 8 2 a. Is w in {v1, V2, V3}? How many vectors are in {v1, V2. V3}? b. How many vectors are in Span{v1, V2, V3}? c. Is w in the subspace spanned by {v1, V2, V3}? Why? a. Is w in {v1, V2. V3}? O A. Vector w is not in {v1, v2, V3} because it is not v1, V2, or v3. O B. Vector w is in {v1, v2, V3} because it is a linear combination of v,, v2, and v3. O C. Vector w is not in {v1, v2, V3} because it is not a linear combination of v1, V2, and v3. O D. Vector w is in {v1, V2, V3} because the subspace generated by v1, V2, and v3 is R°. How many vectors are in {v1, v2, V3}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The number of vectors in {v1, V2, V3} is O B. There are infinitely many vectors in {v1, V2, V3).

U₁ = 4 #0-0 -2,1₂ = and и3 = -32 Note that u₁, ₂ and 3 are orthogonal. V = Given v = 4 -0₁ 2 find the coordinates for v in the subspace Wspanned by 4 4 4 U₁ + -8 -8 U₂ +1 U3|