Consider the linear transformation F ON R^2 defined by F(x,y)= (5x-y, 2x+y) and the following bases of R^2.

E ={ e1, e2}= {(1,0) , (0,1)} and

S= {u1, u2}= {(1,4), (2,7)}

a) Find the matrix A that represents F in the basis E
b) Find the matrix B that represents F in the basis S

i find it confusing..

Question

Consider the linear transformation F ON R^2 defined by F(x,y)= (5x-y, 2x+y) and the following bases of R^2.

E ={ e1, e2}= {(1,0) , (0,1)}  and 

S= {u1, u2}= {(1,4), (2,7)}

a) Find the matrix A that represents F in the basis E
b) Find the matrix B that represents F in the basis S

i  find it confusing..

terenzreignz · Answer

Okay, here's how to do it... but you have to pay real close attention, because this is a sorta surgical process :)
Ready to proceed?

anonymous · Answer

yes

anonymous · Answer

Let's go in steps. The basis E is the canonical base. Do you know how to find the transformation matrix in this case?

anonymous · Answer

What you can do is write the transform of the canonical base and transpose them, put them side by side in a matrix. That is the transform matrix.

anonymous · Answer

For the S base all you have to do is take that transform vectors, write them in the S base coordinates and then transpose them and put them side by side as columns in the transform matrix.

anonymous · Answer

thanks. it helped me