Let F:R2 → R² be defined by F (x, y) (a) Find the matrix A representing F in the usual basis E. (b) Find the matrix B representing F in the basis S {(1,4), (2,9))}. (c) Find P such that B = P-1AP. (4x + 5y, 2x – y). [u1, uz] = %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please solve all parts. its a single question . thank u

Let F:R2 → R² be defined by F (x, y)
(a) Find the matrix A representing F in the usual basis E.
(b) Find the matrix B representing F in the basis S
{(1,4), (2,9))}.
(c) Find P such that B = P¯-1AP.
(d) For
that [F]s[v]s = [F (v)]s.
(4x + 5y, 2x – y).
[u1, uz] =
v = (a, b),
find
[v]s
and [F(v)]s. Verify
IS
Transcribed Image Text:Let F:R2 → R² be defined by F (x, y) (a) Find the matrix A representing F in the usual basis E. (b) Find the matrix B representing F in the basis S {(1,4), (2,9))}. (c) Find P such that B = P¯-1AP. (d) For that [F]s[v]s = [F (v)]s. (4x + 5y, 2x – y). [u1, uz] = v = (a, b), find [v]s and [F(v)]s. Verify IS
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