Question

Let `\mathcal{B} = {[[-2],[-1]][[3],[4]]} = {vecv_1, vecv_2}` find `[vecx]_\mathcal{E}` Knowing that `[vecx]_\mathcal{B}= [[-5],[3]]`?

Let `\mathcal{B} = {[[-2],[-1]][[3],[4]]} = {vecv_1, vecv_2}`
find `[vecx]_\mathcal{E}`

Knowing that

`[vecx]_\mathcal{B}= [[-5],[3]]`?

Answer 1

`(19,17)`.

Explanation:

`vecx` has been represented as `(-5,3)` using the basis vectors

`vecv_1=(-2,-1) and vecv_2=(3,4)`.

Hence, using the usual standard basis,

`vecx=-5vecv_1+3vecv_2`,

`=-5(-2,-1)+3(3,4)`,

`=(10,5)+(9,12)`,

`=(19,17)`.