Find a linear transformation 7: R2 R2 such that 7(1,-2) = (1, 1) and T(0, 1) = (2,3), where B = {(1,-2), (0, 1)) is a basis of IR2.

Question

Find a linear transformation 7: R2 R2 such that 7(1,-2) = (1, 1) and T(0, 1) = (2,3), where B = {(1,-2), (0, 1)) is a basis of IR2.
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Solution 1

To find a linear transformation T: R2 -> R2 such that T(1,-2) = (1, 1) and T(0, 1) = (2,3), we can use the fact that T is completely determined by its action on a basis of R2. In this case, the basis B = {(1,-2), (0, 1)} is given.

Step 1: Write the vectors T(1,-2) and T(0, 1) as column vectors:

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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