How do I explain (in words) that basis B spans V, is linearly independent, and is a basis of V?

Let V be a vector space and basis B = {v1, . . . , vn} a subset of V . In complete sentences, explain what it means that(a) B spans V , if for every v ∈ V there are coefficients a1, . . . , an ∈ R,... more


The derivative of a function of f at x is given by

The derivative of a function of f at x is given byf′(x)=limh→0f(x+h)−f(x)hprovided the limit exists. Use the definition of the derivative to find the derivative of f(x)=7x2+3x+4. Enter the fully... more


Discrete math and structures

Suppose you are managing 17 employees, and you need to form three teams to work on different projects. Assume that all employees will work on a team, and that each employee has the same... more

Prove that mn^k is even if k > 0

Let n, m, k be integers where n is even and m is odd. Prove that mn^k is even if k > 0.I know intuitively that n^k can just be expressed as an even number, because n is even. But is that a valid... more

Discreete mathematics proof

Let n and m be integers and assume that n is even. Prove that nm is even and that n + m has the same parity as m.


altitude and triangle

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/min. At what rate is the base of the triangle changing when the... more

Solve the differential equation using power series

If the series y(x) = Σn=0 to infinity (Cn x^n) is a solution of the differential equation 3y''-3x^2y'+3y=0. A general solution of the same equation can be written as y(x) = C0y1(x) + C1y2(x),... more


i cannot solve this exerccise

Let M = {1, 2, 3, 4, 5, 6, 7, 8, 9}. As usual, denote ¨ P (M): = {A | A ⊆ M} is the power set of M. We consider the maps⊕: P (M) × P (M) → P (M) and *: F2 × P (M) → P (M),byA ⊕ B: = A triangle B... more

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