Question

Pls help. see the attachment for the question.

Answer 1

@JamesJ can u help me pls?

Answer 2

Please is such an underused work on this site.

Answer 3

Let u=i+j+2k, v=3i+j-k and
w=βi+(β-1)j-k where β is a real number.

Find β such that the space spanned by u and v is the same as the space spanned by u and w.

Answer 4

*word

Answer 5

I am sorry I didn't get you.

Answer 6

I am saying thank you for asking with "please", vs. just putting out a demand that I or someone else help you. It's slightly ironic. Don't worry about it.

Down to business. If u and v span the same space as u and w, then they will have the same row reduction.

Answer 7

I.e., the row reduction of
1 1 2
β β-1 -1

will be the same as the row reduction of
3 1 -1
β β-1 -1

Use that fact to find a value of β for which that is true.

Answer 8

If you dnt mind can u tel me vat is row deduction?

Answer 9

Ok, you don't that. Another strategy then.

If the span of the two pairs of vectors is the same, then any vector in one span can be written as the vector in the other. Hence for any vector in the span of u and w,
i.e.,

x = au + bw
where a and b are arbitrary constants.

x is also a member of the span of v and w; i.e., there exist constants c and d such that

x = cv + dw

Answer 10

Now equate those two expressions for the vector x and find what what implies for beta.

Answer 11

You will end up with three equations, one for each component of x. Remember that a and b are arbitrary. This constrains your choice of beta.

Answer 12

Nw I understand it . Thanx a lot. was the way I askd u for the help wrong? If so I am extremely sorry.

Answer 13

You asked *correctly*, using the word 'please'. Please is a very good word.

Answer 14

Thanx a lot again.

Answer 15

hw do arbitary constants limit the choice of beta

Answer 16

After this I am stuck. Can you please tell me how to proceed after this?