Show that if ~w is orthogonal to ~u and ~v, then ~w is orthogonal to every vector ~x in span{~u, ~v}.

Explanation:

is ortogonal to a vector if, and only if, the scalar product Hence, it should be

The scalar product is linear, so it takes constants and sums out. If is a vector spanned by and lets say for certain complex (or real) values a and b, then we have

Because both and are equal to 0. That proves that , an arbitrary element in is perpendicular to .

I hope that helped you!

answer is d-29

step-by-step explanation:

since you didn't include the picture, i can give you the description so you know how to pick the correct answer. the third quartile of a data is always shown in a box plot. in the middle of your graph should be a box. the third quartile is the value that goes with the far right edge of the box.

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.