Let u, v, w be three vectors in R4, with the following properties: {u, v} are linearly indepen- dent, and w is not in the span generated by u and v. Explain why {u, v, w} are, in fact, linearly independent.

Atheater wants to build movable steps that they can use to go on and off the stage. they want the steps to have enough space inside so they can also be used to store props. how much space is inside the steps?