辅导MATH 211、讲解R、linear equations讲解、辅导R编程语言
辅导留学生Prolog|调试Matlab程序
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].