6(a- Use partial integration to find the potential function fassociated with

How did i do? Find the sum of the two vectors shown in the figure. Choose the coreect answer below

Find the distance from y to the plane in R³ spanned by u, and u₂.

Write y as the sum of two orthogonal vectors, one in Span[u] and one orthogonal to u.

Find the centroid of the following cross section. [5 -2 -5 3]

Find bases for Nul A , Col A and Row A where A=[100 020 650 530].

Use determinant to find out whether the given matrix is invertible or not.

Problem 3. Consider a filter h[n]. a) Find the Fourier transform of its autocorrelation sequence a[n] =Σ h[k]h* [k — n] . b) Show that if (h[k – n], h[k]) = δ[n], then c) Show that if |H(jw)| = 1, then |H(e^jw)| = 1, Vw. (h[k — n], h[k]) = 8[n]. d) Show that if |H(e^jw)| = 1, Vw, then {h[k – n], n € Z} is an orthonormal basis for l² (Z).

(a) Is the family 13 = (1, v2, /3) of the elements 1, v2, v3 € R in the Q-vector space R is linear and- dependent? If so, specify the subspace U of R, of which B is a base. What kind Does U have a dimension? (b) Show that R as a vector space over Q has no finite dimension, i.e. dimg R = 00. (Note: Use the fact (without proof) that for k € N the two quantities Qk and R is not equal.)

Problem 4. Consider two waveforms yo[n] and 1 [n] and two waveform o[n] and ₁ [n] in £²(Z). Let ho[n] and h₁ [n] be two filters such that ho[n] = [n] and h₁ [n] = ₁ [n], and go[n] and g₁ [n] two filters such that go [n] = o[n] and gi[n] = ₁ [n].