linear algebra problems

[Sunnyboy]

Consider the linear transformation of R2 which is the result of the successive application of these linear transformations:

the reflection through the line x1=x2, followed by
the rotation by 3*15 degrees (anticlockwise), followed by
the reflection through the x1-axis.

Find the matrix of the linear transformation first. Then answer: what is the top left entry of the matrix?

(The answer is numerical: do not forget to round appropriately.)

 

[叫天不应]

看不懂

 

[Martonical]

出题越来越变态了

 

[Sunnyboy]

Let {v1, v2,...,vp} be a set of linearly independent vectors in Rn. Select all correct statements.


a. The set {v1, v2,...,vp-1} is linearly independent.
b. There are two parallel vectors among the given set of vectors v1, v2,...,vp.
c. n ≥ p
d. One of the vectors can be written as a linear combination of the other vectors.
e. n < p

 

[想哭的眼泪]

别告诉我是1341的课~~~我好像没落这么多阿~~怎么都看不懂了呢

 

[Sunnyboy]

One-to-one and onto linear maps
Let A be a matrix with 9 rows and 9 columns. Suppose that an echelon form of A has 8 pivots. The matrix A determines a linear map that to a vector x assigns the vector Ax. Answer with the appropriate digit:
0
if the map is neither one-to-one nor onto;
1
if the map is one-to-one but not onto;
2
if the map is onto but not one-to-one;
3
if the map is both one-to-one and onto.

 

[Sunnyboy]

最初由 想哭的眼泪 发布
别告诉我是1341的课~~~我好像没落这么多阿~~怎么都看不懂了呢

for math 1104, which is similar to math 1107

 

[Stifler]

A,C

-sin(45)

3

 

[Sunnyboy]

最初由 Assticker 发布
A,C

-sin(45)

3

you sure the answer of the 3rd is 3?

 

[Sunnyboy]

and for the 1st one what if a matrix is {(1,2,9)(2,4,5)(3,6,2)}
but {(1,2)(2,4)(3,6)}is dependent

 

[无忧黄雨]

how about this one?


First of all, find out for which value of the scalar c are the vectors
u= (1, 1, 3),
v= (1, 3, 4),
w= (3, 4, c)
linearly dependent. Using this c, express the vector w as a linear combination of the vectors u and v.
What is the coefficient (the weight) of v in this linear combination?

The vectors are written as rows only for ease of typing.
The answer is numerical, round it appropriately!

 

[Stifler]

你们做了哪些亚。。一共5道

 

[无忧黄雨]

我上个星期看病落了两节课

 

[Stifler]

at least one solution

&
at most one solution

and make sure on dependent and independent

 

[Stifler]

onto, at least one

one to one, at most one