Find a set of columns that fo11n a basis for the column space of each of the following matrices. Give the rank of each matrix. Also find a basis for the null space of each matrix. a) [-3 6 5 -10]
b) [2 1 1 1 2 1 7 5 4]
c) [ 1 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1]
d) [1 1 1 0 1 0 1 0 1 0 2 1 2 -1 2 -1 1 -1 2 -1 1 2 1 1 1]

Circle d circumscribes abc and abe. which statements about the triangles are true? statement i: the perpendicular bisectors of abc intersect at the same point as those of abe. statement ii: the distance from c to d is the same as the distance from d to e. statement iii: bisects cde. statement iv: the angle bisectors of abc intersect at the same point as those of abe. a. i only b. i and ii c. ii and iv d. i and iii e. iii and iv

What is the next step in the given proof? choose the most logical approach. a. statement: m 1 + m 2 + 2(m 3) = 180° reason: angle addition b. statement: m 1 + m 3 = m 2 + m 3 reason: transitive property of equality c. statement: m 1 = m 2 reason: subtraction property of equality d. statement: m 1 + m 2 = m 2 + m 3 reason: substitution property of equality e. statement: 2(m 1) = m 2 + m 3 reason: substitution property of equality

Triangles abc and dfg are given. find the lengths of all other sides of these triangles if: b ∠a≅∠d, ab·dg=ac·df, ac=7 cm, bc=15 cm, fg=20 cm, and df-ab=3 cm.