Creating a transformation matrix This question is related to this one, but more specific. I was given the following question: Let D={d1,d2} and B={b1,b2} be bases for vector spaces V and W respectively. Let T:V→W be a linear transformation with the property that T(d1)=−5b1−7b2 and T(d2)=9b1+4b2. Find the matrix for T relative to D and B. This is a pretty simple question and I just took the transformation properties and made a matrix: (−5−794) The answer key has the same answer but with the rows and columns switched: (−59−74) Are these both correct?

Question

Creating a transformation matrix  This question is related to this one, but more specific. I was given the following question:  Let D={d1,d2} and B={b1,b2}  be bases for vector spaces V and W respectively. Let T:V→W be a linear transformation with the property that T(d1)=−5b1−7b2 and T(d2)=9b1+4b2. Find the matrix for T relative to D and B.  This is a pretty simple question and I just took the transformation properties and made a matrix:  (−5−794)  The answer key has the same answer but with the rows and columns switched:  (−59−74)  Are these both correct?

liofila3w7 · Accepted Answer

The book is correct. Consider applying your matrix to a basis vector:  (−5−794)(10)=(−59)≠(−5−7)  Generally, the i-th column of T corresponds to the image of the i-th basis vector.

Creating a transformation matrix This question is related to this one, but more specific. I was

Answered question

Answer & Explanation

New Questions in Integral Calculus