Solution Found!
Since the coordinate mapping determined by B is a linear
Chapter 4, Problem 21E(choose chapter or problem)
Problem 21E
Since the coordinate mapping determined byB is a linear transformation from into , this mapping must be implemented by some 2 × 2 matrix A. Find it. [Hint: Multiplication by A should transform a vector x into its coordinate vector
Questions & Answers
QUESTION:
Problem 21E
Since the coordinate mapping determined byB is a linear transformation from into , this mapping must be implemented by some 2 × 2 matrix A. Find it. [Hint: Multiplication by A should transform a vector x into its coordinate vector
ANSWER:
Solution 21E
Step 1
Let us suppose that,
Observe that, where
Observe that, the two vectors in are not scalar multiples each other, so these two vectors are linearly independent in and it has dimension 2. So the set forms a basis for
Let
The coordinates of relative to the basis are the weights such that