Question

Consider the bases B={p1,p2} and b'={q1,q2} for p1,where p₁ =6+1x,p₂ =12+14x,q₁ =2,q₂ =1+2x. Find the transition matrix from B to B ' . The transition matrix from B to B ′ is Q=

Answer 1

To find the transition matrix from B to B', use the given relations x' = x cos(q) + y sin(p) and y' = -x sin(p) + y cos(p) to express the vectors p1 and p2 in terms of the vectors q1 and q2. Substitute the values and calculate the transition matrix Q.

Step-by-step explanation:

To find the transition matrix from B to B', we need to express the vectors p1 and p2 in terms of the vectors q1 and q2 using the given relations:

x' = x cos(q) + y sin(p)

y' = -x sin(p) + y cos(p)

Substituting the values p1 = 6+1x, p2 = 12+14x, q1 = 2, and q2 = 1+2x, we can calculate the transition matrix as follows:

For p1:

p'1 = q1 cos(q) + q2 sin(p)

For p2:

p'2 = q1 sin(p) + q2 cos(p)

Therefore, the transition matrix Q is:

Q = [cos(q) sin(p)]

[sin(p) cos(p)]