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Let V be the subspace of all vectors in R 5 , such that x1 −...

Let V be the subspace of all vectors in R 5 , such that x1 − x4 = x2 − 5x5 = 3x3 + x4

(a) Find a matrix A with that space as its Null space; What is the rank of A?

b) Find a basis B1 of V ; What is the dimension of V ?

(c) Find a matrix D with V as its column space. What is the rank of D? To find the rank of D use only the fundamental theorem of Linear Algebra, part I and common sense (No computation is needed!).

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