Posted by Bradley Vrecko on November 05, 2002 at 23:30:29:
In Reply to: Finding the transformation matrix relative to bases.. posted by Bradley Vrecko on November 05, 2002 at 23:12:06:
The answer book gives the following 2X2 Beta matrix [1 5, 0 1] and I just redid the problem and came extremely close.
Using the above method I used an arbitrary matrix [a b, c d] and left multiplied it by [x]B giving a vector [1/5*a + 3/5*b, 1/5*c + 3/5*d] and this vector will equal [T(x)]B so it should be a matter of solving the equations a + 3b = 16 and c + 3d = 3 since I calculated the vector [T(x)]B to be [16/5, 3/5]
I can see that the Beta matrix in the answer book is correct, and I got the second row the same but for my first row I had 10 2 instead of 1 5. They both work and I am wondering if the Beta matrix is unique or am I missing something fundamental?
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