Question

Finding the determinant of the matrix---a system of vectors.

Answer 1

Let me type it..

Answer 2

U=2i+3j+2k
V=-2i+4j-k
W=3i+3k

1. find det. by hand
2. Find values of U, X, and W
3. Explain the orientation of this vector (UXW) in terms of U and V.

Answer 3

ok, so I need to make in Matrix form. Then I can use a general formula I was given. AEI-AHF-BDI+BGF+CDH-CGE. But do I put a 0 in the place of the J for vector w?

Answer 4

If you know the law of Sarrus, you can evaluate the determinant of this 3x3 Matrix that way.

Answer 5

yes you put a 0 there. The "redundant" equation for W is:
\[\Large w=3i+0j+3k \]

Answer 6

Perfect.

Answer 7

And yes, I do know and will use that law.

Answer 8

Thanks for that.
But what in the world are steps 2 and 3 asking?

Answer 9

They probably want you to try and setup a 3x3 system and solve for u,v,w.

Answer 10

like express one in terms of another, this is how I would judge that. For c I am unsure myself, if the determinant is not equal to zero, that means that the vectors aren't linearly depending, that would kind of disassociate with that problem.

Answer 11

True. I guess I just need to work step one. I will tag you when I get it done, I need to step away from my desk for a minute. Thanks.

Answer 12

No problem.

Answer 13

@Spacelimbus the det of the matrix is 9.

Answer 14

http://www.wolframalpha.com/input/?i=find+determinant&f1=%7B%7B2%2C3%2C2%7D%2C%7B-2%2C4%2C-1%7D%2C%7B3%2C0%2C3%7D%7D&x=8&y=6&f=Determinant.detmatrix_%7B%7B2%2C3%2C2%7D%2C%7B-2%2C4%2C-1%7D%2C%7B3%2C0%2C3%7D%7D

Answer 15

@Spacelimbus

Answer 16

true

Answer 17

geometrically that means that the vectors are linearly independent, therefore none of the above given vectors is redundant.

Answer 18

Now I need the values of U, V, and w.

Answer 19

2. Find values of U, X, and W

It says U, X and W. Not U, V and W.

Answer 20

Wait, the top of this post does say u, v, and w.

Answer 21

U=2i+3j+2k
V=-2i+4j-k
W=3i+3k

1. find det. by hand
2. Find values of U, X, and W
3. Explain the orientation of this vector (UXW) in terms of U and V.

This? I copy pasted that from the top. Or you mean on your paper?

Answer 22

right, of that from the top I need to find what U, V, and W are.

Answer 23

and to be honest with you, I haven't seen such a question before myself, have you done something similar to that?

These are vectors, a vector has three properties: Magnitude(Length), Direction and Orientation. I don't think that it makes sense to ask for a value of a vector, especially because they mention the plural form "values" which indicates to me that there are many. Of course, we could always scale the vector - but that makes no sense to me as well.

Maybe someone else can help here, I don't understand what they're asking for.

Answer 24

I agree, but at this point I guess i just want to find U V and W regardless.
U=2i+3j+2k
V=-2i+4j-k
W=3i+3k

But I forgot how.

Answer 25

I opened a new ?.