Please show me steps and solution for all parts!! Let1020-11010 1and let T : R6 → R5 be defined by T(x) = Ax.(a) Find a basis for ran(T). What is dim(ran(T))?(b) Use the Rank-Nullity theorem to find dim(ker(T)).(c) FindA =Ax =basis for ker(T), i.e. a linearly independent set of vectors from ker(T) of sizedim(ker (T)).(d) What are the solution sets to121-2 2-12 1020-31 020102 0036andAx=1 ?

Given matrix is and (a) Obviously basis for is same as basis for column space of A . Now…

Let 1 0 1 2 0 -1 -1 1 0 0 1 1 0 1 1 and let T: R6 →→ R5 be defined by T(x) = At. (a) Find a basis for ran(T). What is dim(ran(T))? (b) Use the Rank-Nullity theorem to find dim(ker(T)). (c) Find a basis for ker(T), i.e. a linearly independent set of vectors from ker(T) of size dim(ker(T)). (d) What are the solution sets to A = Az = -1 -2 2 2 2 0 -3 21022 3600 0 0 and Az = [0] 0 1? 1

Let 1 0 1 2 0 -1 -1 1 0 0 1 1 0 1 1 and let T: R6 →→ R5 be defined by T(x) = At. (a) Find a basis for ran(T). What is dim(ran(T))? (b) Use the Rank-Nullity theorem to find dim(ker(T)). (c) Find a basis for ker(T), i.e. a linearly independent set of vectors from ker(T) of size dim(ker(T)). (d) What are the solution sets to A = Az = -1 -2 2 2 2 0 -3 21022 3600 0 0 and Az = [0] 0 1? 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

See similar textbooks