For #3-8: True or False. If false, explain why. 3. If V1, V2, V3, V4 € IR4 and v3 = 2v1 + V2, then {V1, V2, V3, V4} is linearly dependent. this is true, Vs is a linear combination of 1₁ and 1₂ 4. If V₁, V2, V3, V4 € R4 and v₂ = 0, then {V₁, V2, V3, V4} is linearly independent. This is false bes a zero vector with make 1 column unable to have a which will have a free variable =) Linearly Dependent 5. If v₁ and v₂ are nonzero vectors in R5 and v₂ is not a scalar multiple of V₁, then {V₁, V₂ } is linearly independent. 6. If V₁, V2, V3, V4 € R4 and v₂ is not a linear combination of V₁, V3, V4, then {V₁, V2, V3, V4} is linearly independent. This is false, V3 V4, on v₁ can all be linear combinations of each other pivot 7. If V1, V2, V3, V4 € R4 and {V₁, V2, V3} is linearly dependent, then {V₁, V2, V3, V4} is also linearly dependent. 8. If V₁, V2, V3, V4 € R4 and {V₁, V2, V3, V4} is linearly independent, then {V₁, V2, V3 } is also linearly independent. This is false bes it is possible V4 oan be a linear combination of the other vectors (V₁, V2103) 9. Let A be an mxn matrix, and let u,ve Rn, such that Au = 0 and Av = 0. Do not skip steps. State theorems used in supporting reasoning. (b) Show that A(cu + dv) = 0 for scalars c and d. Let Autò and A=0 A'((ut + d) where C, and I are scalars = A. (cu) + A (du) (Matrix multiplication distribute over addition ²)+(AF) d (a) Show that A(u + v) must be the zero vector.