Question

Time Remaining: 01:56:51 Submit Test Test: Math 410 Chapter 4 Test This Question: 1 pt 9 of 11 This Test: 25 pts possible Show that if {v1...vp} is linearly dependent in V, then the set of images, {(M1. T()}. is linearly dependent in W. This fact shows that if a linear transformation maps a set {...} onto a linearly independent set {T (1) T()}, then the original set is linearly independent, too (because it cannot be linearly dependent.) B IŲ SIX E 들 - E 1 X Insert Formula

Answer 1

* apyllp, 9,921-44, 4R hiven that {9, U2, ... Ups is linearly dependent in U. then we write one vector from above set in the combination of other veetorse let Umt {U,,Uzi Up} then Um = a,l,tq2U 2+ apply linear Trasformation both sidle TCum) : Tlaid,+9 42+ - +9px 0p] know that T (autbe) = T(Vm) = 9,T(U) + 92T (U2) t- tap-iT( Up) from this we can say that Teu), FLUR) - Tum) , .. TU pl} is a linearly dependent set in to and we know that convesse of this is also true = It a linear transformation map a set 14, 2, - - Up} onto linearly independent set { T(0,), ILO) - Tup)) then the original set is linearly independent- a[14) tbllo) هلا "Hence proved".