given this vectorial space V= what value does "a" needs to have so that v=(a,2,4,7). belongs to V

Question

given this vectorial space 
V=< (0, 0, 0, 1), (0, 0, 1, 2), (1, 2, 3, 4)>
what value does "a" needs to have so that  v=(a,2,4,7). belongs to V

anonymous · Answer

@Micah1mcdugle

amistre64 · Answer

do you know what an rref is?

anonymous · Answer

no :/

amistre64 · Answer

it is the augmented matrix (A:b) which results in the solution for of (I:x)

anonymous · Answer

wow im sorry pay attention

anonymous · Answer

well now im confused u.u

anonymous · Answer

im paying attention to im mean

anonymous · Answer

pardon?

anonymous · Answer

sorry im confused but I was working on something similar too. sorry

amistre64 · Answer

we can work it up as:

1 0 0 a
2 0 0 2
3 1 0 4
4 2 1 7


and reduce the row echelon form to solve for a

anonymous · Answer

why are you using the 1 2 3 4 first?

amistre64 · Answer

no particular reason, was easier for these old brain to remember first i spose

rational · Answer

because the order in which you put the vectors  doesn't matter for column space
```
1 0 0 a 
2 0 0 2 
3 1 0 4 
4 2 1 7
```

amistre64 · Answer

youre welcome

rational · Answer

there is a shortcut/eyeballing thing here if we're careful.. 

Notice that we have only one line (1,2) in the plane represented by first two components

`1 0 0` 
`2 0 0`
3 1 0 
4 2 1

so you can only reach the points on this line in the plane represented by first two components

rational · Answer

$$\large \dfrac{1}{2} = \dfrac{a}{2}$$

you can solve  $a$