1. ## 2 problems I need urgent answers for!

I've been staring at these two problems for hours and I can't seem to figure them out. They seem to have nothing to do with the rest of the problem set and my professor said nothing about them in class... Will give a million thanks a kiss in advance!

1. Let [-7 1 1 -7]

Find a basis of the subspace of consisting of all vectors perpendicular to .

[_ _ _ _ ], [_ _ _ _ ], [_ _ _ _ ]

2.

Let be the basis of consisting of the vectors
[5 -3] and [2 5] ,

and let be the basis consisting of

[-2 1] and [3 -2 ] .
Find a matrix such that for all in .

[_ _] <-----(2x2 matrix)
[_ _]

(All vectors should be column vectors, I had to change them because they didn't copy right)

2. Originally Posted by elven06
I've been staring at these two problems for hours and I can't seem to figure them out. They seem to have nothing to do with the rest of the problem set and my professor said nothing about them in class... Will give a million thanks a kiss in advance!

1. Let [-7 1 1 -7]

Find a basis of the subspace of consisting of all vectors perpendicular to .

[_ _ _ _ ], [_ _ _ _ ], [_ _ _ _ ]

You have to find a basis for the solution space of $\displaystyle -7x_1+x_2+x_3-7x_4=0$ (why?). This basis is what you want.

2.

Let be the basis of consisting of the vectors
[5 -3] and [2 5] ,

and let be the basis consisting of

[-2 1] and [3 -2 ] .
Find a matrix such that for all in .

[_ _] <-----(2x2 matrix)
[_ _]

You have to find the matrix of the transformation that maps one basis into the other one (transition map/matrix)...

Tonio

(All vectors should be column vectors, I had to change them because they didn't copy right)

.

3. Ok. so making x1, x2, x3, x4 into a b c d

I got that:

a = b/7 + c/7 - d

b = 7a - c + 7d

c = 7a - b +7d

d = -a + b/7 + c/7

I think this is progress, however, I still don't know how to find what I need...

as for the second problem, I have no idea how to go about that at all. I've never really heard of what you mentioned...

4. Originally Posted by elven06
Ok. so making x1, x2, x3, x4 into a b c d

I got that:

a = b/7 + c/7 - d

b = 7a - c + 7d

c = 7a - b +7d

d = -a + b/7 + c/7

I think this is progress, however, I still don't know how to find what I need...

as for the second problem, I have no idea how to go about that at all. I've never really heard of what you mentioned...

It seems then like you're trying to solve problems about stuff you haven't yet learned about or already forgot, and that can't be good. Read again about this stuff, since this is very important in particular if you're taking a linear algebra course: you're gonna need it bad.

Tonio