Linear algebra -->Vector spaces

[hayood]

Express (-9,-7,-15) as a linear combination of u=(0,-2,2) v=(1,-1,3) and w =(3,2,5)


this is what i did so far:

(-9, -7, -15)= k1(2,1,4)+k2(1,-1,3) k3(3,2,5)

(-9, -7 -15)= (2k1+k2 +3k3, k1-k2 +5k3, 4k1+3k2+5k3)

2k1+k2+3k3 =-9
k1 -k2 +5k3 = -7
4k1+3k2+5k3 = -15


what should i do next? Gaussian elimination?

 

[daon]

Yes, but where did (2,1,4) come from?

 

[hayood]

sorry i mistyped u.. u=(2,1,4)


when i did gaussian elimination i got a wrong answer

 

[mmm4444bot]

??

2k1 + k2 + 3k3 = -9

k1 - k2 + 5k3 = -7 The number 5 is another typographical error, yes?

4k1 + 3k2 + 5k3 = -15

??
I get the following values.

k1 = -2

k2 = 1

k3 = -2

If these are the values that you expect to get, too, then check your arithmetic in the Gauss-Jordan steps.

BTW, this site has a [Preview] button to the left of the [Submit] button. I suggest that you start using it, to proofread your typing before posting.

??

 

[hayood]

oh ya sorry it should be -7.
thanks anyways.
lol i'll make sure to review my posts next time b4 submitting

 

[Denis]

i'll make sure to review my posts next time b4 submitting

What does b4 mean; b to the power 4 ?

 

[mmm4444bot]

??

oh ya sorry it should be -7. Huh?

??
I was thinking that that 5 should be 2, not -7.

Now, I'm confused.

??

 

[hayood]

this is the question again

Express (-9,-7,-15) as a linear combination of u=(2,1,4) v=(1,-1,3) and w =(3,2,5)

 

[hayood]

b4 means before lol.