2008 Second Semester MATHS课程问答帖(请用英文提问)

duclover

can i ask some questions from maths 208???

Let U consist of all vectors in 3-dimensional Euclidean vector space R3 each of whose entries

is the same, that is U = {f(a; b; c) : a = b = c }
State a system of linear equations that de nes U.



what's that mean???

thanks~

duclover

i still donn't understand how to
State a system of linear equations that defines U
in this quextion.....

duclover

In each of the following two cases, the set of vectors {v1,....,vn} forms an orthonormal
basis for the corresponding Euclidean vector space Rn.
Find an expression for the given vector w in terms of this basis.
(Do not use Gaussian elimination.)


Q:n = 2, v1 = [1/root2    1/root2]T, v2=[-1/root2   1/root2]T,   w=[9 4]T

(T means transpose)

摇得你好滚

(c) hint: what does (a,a) look like, x=a, y=a => x=y, over here you got x=y=z
(d) see previous answers. should be obvious now.
.......?

still don't understand....x=y means a line through origin and form 45 degree angle with x-axis? then what about x=y=z?

摇得你好滚

and for Q6, is it using the formula of  w=(w * v1)v1+(w * v2)v2+......+(w * vk)vk ?

uwantsprincess

Anyone know how to do Question 1a, 1b??

摇得你好滚

but what if i write like this:
a1*v1+a2*v2=w,  and v1, v2, w are all known, so could solve a1 and a2, hence could get a equation like this:
              w= ((13√2)/2)*v1-((5√2)/2)*v2
..........?

摇得你好滚

thanks, our lector just start topic 5 this morning so got it now

clement001

A piecewise function f is defined by:
f(x) = x + k when x is less than 1, and
f(x) = 3 otherwise.
What value of k makes f continuous at x = 1?

a.  3
b.  1
c   2
d   no value of k




HOW TO CALCULATE
i have no idea

摇得你好滚

Queation:  Find the characteristic equation for the matrix A:
                                        1  2  1
                                  A = 1  0  1
                                         1  6  1

THX.

bendy1111

maths 108

question 8

consider the function defined by h(x)=1/(sqr(x^2 -k), where k is a constant.

a) find a value of k for which  h has no vertical asymptotes.
b) how does the natural domain of h depend on the value of k?
c) what valuees of k give h two vertical asymptote?

help me plz

akl

Maths 108 Assignment 1

Question 6 (b) (c) (d)

How do u type in the commands in the Matlab? Thanks!

册那

maths250 assignment1 question 9.
Let n>=3. which of the following sets of vectors u = (x1,...,xn) in R^n are subspaces of R^n?
(a)all u such that x1>=0
give reasons to your answer.

cheers.

江儿

math162 Q3 b

没蚊香的黑夜

Help plz with MATHS 208

A =

1 2 0
2 1 0
0 0 4
.
Find an orthogonal diagonalisation of A. That is ...
(a) Find the eigenvalues.
(b) For each eigenvalue, find an eigenvector.
(c) Normalize each eigenvector. (Make it have unit length.)
(d) Check that in this case the 3 eigenvectors are orthogonal.
(e) Diagonalize A, so that
A = CDCT ,
where C is an orthogonal matrix. (For orthogonal matrices C−1 = CT .)

I  can only find one eigenvalue which is 4.......but in (d), it seems like there should be 3 eigenvalues.....anybody help with this question?

摇得你好滚

Given the linear system
                                          (1    1    1)                     (5)
                                          (1    1    0)      (x1)         (4)
                              Ax =                             (x2)    =
                                           (0    1    1)      (x3)         (4)
                                           (1    0    1)                      (4)
How to show that this system is inconsistent?

Why do i get it is consistent after i row reduce it.......?

And what is the difference between "calculate the normal system" and "solve the normal system"?