Question

Prove vector i, j, and k spans R^3

Answer 1

To show that:\[\mbox{span}\{i,j,k\}=\mathbb{R}^3\]you need to show that no matter what vector\[\left(\begin{matrix}x_1 \\ x_2 \\ x_3\end{matrix}\right)\]you have in R^3, you can write it as some linear combination of the vectors i, j and k.

Answer 2

@joemath314159 i know that... i got started as
For any vector u which is an element of R^3, where vector u is the addition of the three vectors.

Answer 3

alright, but what three vectors? and furthermore, how much of each of those three vectors? If you can answer those two questions, then you will have proved your statement.