Question

Lets(e)be the standard basis for R with associated xy-coordinate system Showthat - ,d 2) arebases for P2 Let the ry coordinate system be associated with B andthe Find a match for each item in the choices coordinate system be associated with B Choose Choose. Transtion mati from 5 to B" Wat are the y-coordinates of point X f ts x'y"-cocrdnates are (3,4) What are the x-coordinates of point Xiffts xy'-coondinates are (5.7 What are the 'y -coordinates of point Xif ts xy-cocrdnates are (2-5) atrix by which xY coordinates are mubipied to olbtain xy coordirates Tanstion mati from S to B' atix by which xy-cordinates are mutipled to cotain x -coordrates Matix by which xy-coordinates are muitoled to obtan x'y "-coordinates Wat are the xy-cocrdinates of point X ffts xy-coardinates are (9,3) Matrix by which xy-cordinates are mutipled to cotain x'y-coordinate Choose Choose (17/5,-9/5) Choos8 15,10) choose 19, 3 Choose .6 Choose

Answer 1

Given, B' = {u₁,u₂} and B'' = {v₁,v₂}.

Here, u₁ and u₂ are linearly independent and any vector of R² can be spanned by {u₁,u₂}.

Therefore, B' = {u₁,u₂} are bases of R².

Here, v₁ and v₂ are linearly independent and any vector of R² can be spanned by {v₁,v₂}.

Therefore, B'' = {v₁,v₂} are bases of R².

i) $\begin{bmatrix} 1 & 1\\ 0 & 1 \end{bmatrix}$ : Transition matrix from S to B'.

ii) $\begin{bmatrix} 1 & 2\\ 2 & 1 \end{bmatrix}$ : Transition matrix from S to B''.