Linear Transformation

  • Thread starter jlucas134
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Need some help getting started...

Let T ={ [1, 0], [1, 1] }be a basis for R2 .
Given that Transition matrix P s←t
[ 2, 3 ; -1, 2],

find the basis S for R2.

Here is what I think...I started by letting v being any vector...

[1,0] and [0,1] and applied them to the transition matrix by multiplying the transition matrix to each individual set list at the beginning of this sentence to find the v value... to get [2,-1] and [3, 2]

Then taking these values to the vectors of T

I get 2*[1,0]-1*[1,1] and
3*[1,0]+2*[1,1]

My final answer came up with [1, -1] and [5, 2], so is this the basis of S?


2)
Let S ={ [1, -1], [1, 1] } be a basis for R2 .
Given that Transition matrix P s←t

[ 1, 2; 2, 3]

find the basis T for R2.

I think you have to inverse the trans matrix then do the steps from problem one...I get T={[-1,5], [1,-3]} for basis.
 

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