Question

Let AequalsStartSet Bold a 1 comma Bold a 2 comma Bold a 3 EndSet and BequalsStartSet Bold b 1 comma Bold b 2 comma Bold b 3 EndSet be bases for a vector space​ V, and suppose Bold b 1 equals 4 Bold a 1 minus 3 Bold a 3​, Bold b 2 equals negative Bold a 1 plus Bold a 2​, Bold b 3 equals Bold a 1 plus Bold a 2 plus 5 Bold a 3. a. Find the​ change-of-coordinates matrix from Upper B to Upper A. b. Find left bracket Bold x right bracket Subscript Upper A for Bold x equals Bold b 1 minus 4 Bold b 2 plus 4 Bold b 3.

Answer 1

Answer Step-by-step explanation:

Given Data;

Let A = { a₁, a₂, a₃}

B={ b₁, b₂, b₃}

b₁ = 4a₁ - 3a₃

b₂ = -a₁ + a₂

b₃ = a₁ + a₂ + 5a₃

(a) Find the change of coordinates matrix from B to A

[ The matrix portion is attached ]