Solution to Self-quiz 26 in MATH 310: Finding Transition Matrix and Determinant, Quizzes of Linear Algebra

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MATH 310

Self-quiz 26

1. Find the transition matrix from the basis:

[

T , (2, −1)

T

]

to the basis:

[

T , (0, 1)

T

]

1. Compute the determinant

MATH 310

Self-quiz 26

1. Find the transition matrix from the basis:

[

T , (2, −1)

T

]

to the basis:

[

T , (0, 1)

T

]

Solution: For our convenience, set:

u =

[

T , (2, −1)

T

]

v =

[

T , (0, 1)

T

]

Consider the matrices:

U =

V =

Then U takes us from u to the canonical basis and V takes us from v to the

canonical basis. This means that V

− 1 U will be taking us from u to v.

We have:

V

− 1

and

V

− 1 U =

R 3 + R 1

9 R 1 + R 2

2 R 1 + R 3