2
$\begingroup$

$$\{(1,0,0)^T, (0,1,1)^T, (1,0,1)^T, (1,2,3)^T\}$$

What I did first was write the linear combination of these vectors which I do not know how to format on here but is simply:

$$c_1(1,0,0) + c_2(0,1,1) + c_3(1,0,1) + c_4(1,2,3) = (x, y, z)$$

where the vectors are column vectors.

Then I get the equations $c_1 + c_3 + c_4 = x, c_2 + 2c_4 = y, c_2 + c_3 + 3c_4 = z$.

And this is where I get stuck. How do I prove that the vectors span $\Bbb R^3$ from here?

  • 0
    A simple way to prove a span would be to show how each of the three standard basis vectors can me made as a linear combination of your set.2012-10-02

2 Answers 2