Let M = 0 3 -2 M takes vectors in Rm to vectors in R", where m Mu + Mv = ( M(cu) = = M(u + v) = = c(Mu) = -27 -2,u = ‚ u = (x, y), v = (z, w). Find the following. = 1 Check all that apply. OM(u + v) ‡ Mu + Mv OM(cu) + cMu OM is a linear transformation 1.0 and n

Please justify whether these statements are true of false. a. If u and v are vectors in R^3, then IIu-vII less than or equal to IIuII - IIvII b. Let u, v, and w be non zero vectors in R^n. If u and v are parallel to w, then 5u-v is also parallel to w

How do I find the magnitude of  <-2, 1, 2> this vector?

EXAMPLE 5 Vectors in R' Let u = (2, –4, 1) and v = ponents of the following vectors and draw them in R. (3, 0, – 1). Find the com- 1 b. -2v c. u + 2v а.

Sketch the given vector with initial point (1, 6). u = (-7, -4) 10 y 10 - 10 10 -10 15 10 10 10 -10 15 10 -10 15 X 10 10 Find the terminal point. (x, Y) = (_

. Assuming the +x-axis is horizontal to the right for the vectors in the following figure, find the following scalar products:  (a)   →A · →C  ; (b) →A · →F;  (c)   →D  ·  →C  ;  (d) →A · (→F   + 2 →C); (e) ^i · →B; (f) ^j · →B;  (e) (3 ^i − ^j) · →B, and (h) B^ · B→.