Solutions to Homework 2
... 2. Prove that the set of functions β = {1, cos x, cos2 x, . . . , cos6 x} is linearly independent in C(R). (Hint: Suppose c0 · 1 + c1 · cos x + · · · + c6 · cos6 x = 0. Then this equation holds for all values of x. Hence, for each value you substitute in for x, you get a different linear equation in ...
... 2. Prove that the set of functions β = {1, cos x, cos2 x, . . . , cos6 x} is linearly independent in C(R). (Hint: Suppose c0 · 1 + c1 · cos x + · · · + c6 · cos6 x = 0. Then this equation holds for all values of x. Hence, for each value you substitute in for x, you get a different linear equation in ...
Matrix Groups - Bard Math Site
... For the remainder of these notes, we will only be considering vectors and matrices over the real numbers. Let Rn denote n-dimensional Euclidean space, i.e. the set of all column vectors with n components. For example, R2 is the Euclidean plane, and R3 is threedimensional Euclidean space. If A is an ...
... For the remainder of these notes, we will only be considering vectors and matrices over the real numbers. Let Rn denote n-dimensional Euclidean space, i.e. the set of all column vectors with n components. For example, R2 is the Euclidean plane, and R3 is threedimensional Euclidean space. If A is an ...
Definition: Let S be a nonempty subset of V . Then the span of S is
... Remark: Actually carrying this out in practice may depend on how much information you have about V . Now suppose that (w1, · · · wm) independent sequence in V (eg with (w1, · · · wm) spans V , it is a basis. is a v ∈ V but not in the span, and – Typeset by FoilTEX – ...
... Remark: Actually carrying this out in practice may depend on how much information you have about V . Now suppose that (w1, · · · wm) independent sequence in V (eg with (w1, · · · wm) spans V , it is a basis. is a v ∈ V but not in the span, and – Typeset by FoilTEX – ...
