Span Worksheet with Answer Key

What's on the worksheet

1. Describe each span as the origin alone, a line through the origin, a plane through the origin, or all of R² or R³.
   \operatorname{span}\{(2, 5), (-1, 3)\}\operatorname{span}\{(-2, 4, -6), (3, -6, 9)\}\operatorname{span}\{(1, 0, 2), (0, 3, 0), (2, 3, 4)\}\operatorname{span}\{(1, 1, 0), (0, 1, 1), (1, 0, 1)\}\operatorname{span}\{(3, -1, 2, 0)\}
2. Let v_1 = (1, -2, -3) and v_2 = (-2, 5, 8) in R³.
3. For a number h, let v_1 = (1, h, 2) and v_2 = (h, 4, 2h) in R³.
4. Let v_1 = (1, 1, 0, 1), v_2 = (-2, 0, 1, 2), v_3 = (0, 2, 1, -1) and v_4 = (3, 1, -1, 2) in R^4, and let e_1, e_2, e_3, e_4 be the standard vectors…
5. Decide whether each statement about vectors in R³ is true or false.
6. Priya's office has three rooms on one air system with two dampers.