Let ū== = [1,2,0]T and 7 = = [1,0, 3]T. (a) (2 points) What is span{u, u}? (You can describe this algebraically, geometrically, or in your own words; but be precise!) span {u, v'} Spon { [] [] [] * span 2 (64)-(6)] -2 3 03 both they are Linearly inslependent independent in 7R3, there fore both vector form or plane in Ph ³. (b) (3 points) Show that the vector w = [8, 10,9] is in span{ū,v}. GU + G V =. W 1 78 705 [][ 2 16 39 ][ :) 60 o there is no pivol column in in therefore the w is in the pan { 0,0} (c) (3 points) Is the set {u,, w} linearly independent or linearly dependent? Make sure to justify your answer. ue can as from per (6) the w we could get linear dependant from the {v} الله

1 0 0 1 -4 -5 A = -3 0 12 1 5 -29 10 Which of the following are true? {{)( 4 -2 I. N(A) = span 1 1 1 1 II. R(A) = span -3 1 1 1 III. N(A) = span %3D -4 5 3 -13 -5 IV. C(A) = span А. I, II, only. В. , only. С. II, only. D. II, III, IV, only. E. I. only

Answer T or F and justify your answers (a)* Under a translation, when one point of a figure travels a distance of 5 units, all points of the figure travel a distance of 5 units. (b) If we reflect an object touching a line & about {, all points of the object on { are fixed. (c) If we rotate a figure about a point P, we get a congruent figure. (d) If we dilate a figure using a point P as the center of dilation, we get a similar figure.

Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector 1 Which of the following points (given by their coordinates) lie on | 1? Select one: a. (-3, 1, -1) b. (-2, -1, 0) c. (-3, 2,-1) d. (-4, 3, 0)

Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y² − 6x − 2y² + 2