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- A = [-2,4,-2,-4, 2,-6,-3,1, -3,8,2,-3, 0,2,5,3] Find a non-zero vector R^4 that is an element of both Nul(A) and Col(A) or explain why it is not possible to do so.Define' a vector to contain 2 components: (a,b) where a a rational number, b is an irrational number. Let S? be a set that contains such vectors, ie. s*={ (a,b)| for all rational numbers a, irrational numbers b}. For example, (3.14,71) is in S², but (e,71) is not in S² – 1 & e are well known math constants. Is S a vector space over the integers?Please express H in vector form as well
- Describe the translation the Maps each preimage to its image in (a) coordinates notation and (b) as a vector in components formLet ^-40 A Find a unit vector x whose first component is positive at which Ax has maximum length. Enter the components of x (in order) into the answer box below, separated with a comma.b / Let u and v be a nonzero vectors in 3- space, and let 6 be the angle between these vectors when they are positioned so their initial points coincide. Prove that ux v= sin @