代写MATH 211、代做R、linear equations代做、代写R编程语言

日期：2019-02-26 09:22

MATH 211 201901 Assignment #3

Due on Wednesday February 27, in class

1. [10] Show that the matrix [10] Let ~xT = (x1, x2, . . . , xn) be a row vector in R, and A be a matrix of size n × m.

Show that ~xTA is a linear combination of the rows of the matrix A.

3. [10] Find a matrix A such that .

(Hint: write this equation as a system of linear equations about the entries of A).

4. [10] Let A =

(a) [6] Compute A2

, A3

, and A4

.

(b) [4] Based on your answer to Part (a), give a formula for An

, where n is any positive

integer. (You do not need to prove that your formula is correct).

5. [12] Let L.

(a) [4] Prove the L and G are linear maps

(b) [8] Find the standard matrix (i.e., the matrix representation) of the composite

map G L.

6. [8] Given a vector ~v 6= 0 in R

2

, we can define a projection map P : R

2 → R

2 as

P(~x) = proj~v~x. Find the standard matrix (i.e., the matrix representation) [P].