Suppose that T is a one-to-one transformation, so that an equation T(u)=T(v) always implies u=v. Show that if the set of images {T(v1)T(vp)} is linearly dependent, then {v1vp} is linearly dependent. This fact shows that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set (because in this case the set of images cannot be linearly dependent).

If a and −a are numbers on the number line, which expression must give the distance between them? a) 0 b) a c) |2a| d) |a|

Klmn and pqrs are similar trapezoids. which side of pqrs corresponds to lm

Ican interpret and represent the remainder in division calculations sensibly for the context (eg if we wont to know how many 40 seat buses will be needed to transport 170 students for on excursion, we divide 170 by 40 and realise buses and another smaller vehicle to that we need 4 transport 10 more students) solve the following questions. show your work! 11) the zoo had 420 butterflies that needed to be transported to a new enclosure. the boxes that the butterflies would be moved in only hold 80 butterflies in each. how many boxes would they need? 2 12) each classroom in the school can have exactly 25 students, if there are 345 students in the school how many full classrooms are there?