Week 13

Question 1

(V)B’?

Answer 1

P B->B’ (V)B

Question 2

P B->B’ ?

Answer 2

(f1) B’ , (f2)B’ ….

Question 3

Way to work out P B->B’ using inverse?

Answer 3

P^-1 B’->B

Question 4

P B->E and P E->B alt way to denote?

Answer 4

P B and P B^-1

Question 5

Alt way to work out P B->B’?

Answer 5

P B->B’ = P^-1 B’ P(B)

Question 6

AT B->B?
AT?

If using standard ordered basis as other basis

Answer 6

AT B->B = (P^-1B) (AT) (PB)
AT= (PB) (AT B->B) (P^-1B)

Question 7

IF cannot work out (V)B just off inspection?

Answer 7

Use (V)B= P^-1B (V)

where P^-1B = P E->B

Question 8

In general similarity relation?

Answer 8

AT B1->B1 = P^-1 B1->B2 AT B2->B2 P B1->B2

Question 9

Diagonal matrix?

Answer 9

Diagonal numbers and 0 elsewhere

Question 10

Diagonalise A?

Answer 10

P D P^-1

where D is diagonal

Question 11

How to diagonalise A?

Answer 11

Find eigenvalues using l A - λI l = 0

Then find eigenspaces using N(A-λI)

then write in form PDP^-1

Question 12

ACW rot matrix?

Answer 12

( cos θ -sin θ )
( sin θ cos θ)

Question 13

Ellipse eq?

Answer 13

X^2/a^2 + Y^2/b^2 = 1

where b is x axis intercept and a is y axis intercept++

Question 14

If trying to calc As B->B (what do we put first)?

Answer 14

we put inverse first P^-1 B->E

then if trying to calc As then we put P B->E first

Question 15

For A = PDP^-1? how to get D

Answer 15

Diagonal matrix with eigenvalues as entries