= Consider the basis B₁ = {(1, 0, 0), (1, 1, 0), (1, 1, 1)} of R³ and the basis B₂: – 2), (3, -1)} of R². Define T: R² → R³ such that T((a, b)) = (a + 2b, may assume that T is linear. -a, -b). . Find the matrix M(T) for T with respect to the standard bases in the domain and codomain. ». Find the matrix M(T) for T with respect to B₂ in the domain and B₁ in the codomain.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the basis B₁ =
{(1,2), (3, -1)} of R2. Define T: R²
=
{(1, 0, 0), (1, 1, 0), (1, 1, 1)} of R³ and the basis B₂:
R³ such that
T((a, b)) = (a + 2b, -
You may assume that T is linear.
-a, -b).
a. Find the matrix M(T) for T with respect to the standard bases in the domain and
codomain.
b. Find the matrix M(T) for T with respect to B₂ in the domain and B₁ in the codomain.
Transcribed Image Text:Consider the basis B₁ = {(1,2), (3, -1)} of R2. Define T: R² = {(1, 0, 0), (1, 1, 0), (1, 1, 1)} of R³ and the basis B₂: R³ such that T((a, b)) = (a + 2b, - You may assume that T is linear. -a, -b). a. Find the matrix M(T) for T with respect to the standard bases in the domain and codomain. b. Find the matrix M(T) for T with respect to B₂ in the domain and B₁ in the codomain.
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