Thread: Determine if the given vectors span R4

1. Determine if the given vectors span R4

In each case determine if the given vectors span R4. Support your answer.
{[1 1 1 1], [0 1 1 1], [0 0 1 1], [0 0 0 1]}.

2. One way: express:

$(x_1,x_2,x_3,x_4)=\lambda_1(1,1,1,1)+\ldots+\lambd a_4(0,0,0,1)\quad (*)$

and prove that for all $(x_1,\ldots,x_4)$ the system $(*)$ has solution on the unknowns $\lambda_1,\ldots,\lambda_4$ .

Fernando Revilla

3. Another (simpler) way: Let the given vectors be $v_1, v_2, v_3, v_4$.

$\{v_1-v_2,v_2-v_3,v_3-v_4,v_4\}=\{(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1 )\}$, which is the standard basis in $R^4$.