linear algebra: co-ordinate change matrix?

Question

How do i find this co-ordinate change matrix, and any co-ordinate change matrix in general?

In R^2 find the coordinate change matrix from the basis B1={(2,1)(2,0)} to the basis B2={(–2,–1),(0,1)}

Answer 1

Firstly, there is a formula. However, its quite easy to forget - so why not learn how to actually come up with it?
Suppose you are given coordinates (a,b) in the first system. That really corresponds to the point a[2,1] + b[2,0]. Writing that in matrix form, we have: (// denoting next line)
[2 2 // 1 0][a // b]
Now, we want to express it as c[-2,-1]+d[0,1]. Writing that in matrix form we have:
[-2 0 // -1 1][c // d].
So how do we work out [c // d]? Just multiply on the left by the inverse of that second matrix.
So it would be [-2 0 // -1 1]^(-1) * [2 2 // 1 0].
That turns out to be [-1 -1 // 0 -1].

Answer 2

You need to solve the set of equations corresponding to the matrix arithmetic B2=T B1 and subject to the constraint that the columns of T are orthonormal. This should give you enough constraints to solve for each component of T.

Answer 3

i detect it effective to place in writing out a the matrix equation yet with the matrix empty i.e. (* * *)( a million ) (5-x) (* * *)( x ) = (6+x) (* * *)(x^2) (a million+3x+x^2) Then in case you bypass with the aid of how the matrix multiplication works you have to be waiting to filll in the matrix to get (5 -a million 0) (6 a million 0) (a million 3 a million)

Answer 4

sorry only in 12th grade
lol