Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 1 / 2B (Vectors and Matrices)

Table of contents
- Solution 2B

Solution

Let

P_{B}, P_{B^{'}}, P_{C}, P_{C^{'}}

have the corresponding basis vectors as columns in standard coordinates. From the PDF,

P_{B} = (02 - 2 0), P_{B^{'}} = (11 1 - 1), P_{C} = 110010001, P_{C^{'}} = I_{3} .

The matrix representation of a linear map in standard coordinates is

P_{C} A P_{B}^{- 1}

. The change of basis formula therefore gives

A^{'} = P_{C^{'}}^{- 1} P_{C} A P_{B}^{- 1} P_{B^{'}} .

Multiplication yields

A^{'} = 3/2 5/2 - 1 - 1/2 - 3/2 0 .

 Ancestors (9)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version