Let B = {B₁ = [], B₂ = 1²²= 1·²=6 D be a basis of M2x2 (R). Suppose that T: M₂×2 (R) → P₂(R) is a linear transformation, such that T(ß₁) = x²,T(ß₂) = 1 + x, T (B3) = 2 + x − x²,T(B₁) = −1+x. (a) Find a matrix Z € M3×4 (R), such that if y = Σ½-₁ a¿ß¡, then T(y) = Σ²-o b₁x¹, for some b¡ E [αί R, which satisfies b₁ = Z (b) Find T ([a b]). C a2 a 3 a4
Let B = {B₁ = [], B₂ = 1²²= 1·²=6 D be a basis of M2x2 (R). Suppose that T: M₂×2 (R) → P₂(R) is a linear transformation, such that T(ß₁) = x²,T(ß₂) = 1 + x, T (B3) = 2 + x − x²,T(B₁) = −1+x. (a) Find a matrix Z € M3×4 (R), such that if y = Σ½-₁ a¿ß¡, then T(y) = Σ²-o b₁x¹, for some b¡ E [αί R, which satisfies b₁ = Z (b) Find T ([a b]). C a2 a 3 a4
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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![Let B = {B₁ = [], B₂ = 1²²= 1·²=6 D be a basis of M2x2 (R).
Suppose that T: M₂×2 (R) → P₂(R) is a linear transformation, such that T(ß₁) = x²,T(ß₂) = 1 +
x, T (B3) = 2 + x − x²,T(B₁) = −1+x.
(a) Find a matrix Z € M3×4 (R), such that if y = Σ½-₁ a¿ß¡, then T(y) = Σ²-o b₁x¹, for some b¡ E
[αί
R, which satisfies b₁ = Z
(b) Find T ([a b]).
C
a2
a 3
a4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1811f2be-b76f-4355-a868-605eb1f94cd4%2Fae619f1d-fd59-462c-84a0-49636489ec5d%2Fp7rk2z1_processed.png&w=3840&q=75)
Transcribed Image Text:Let B = {B₁ = [], B₂ = 1²²= 1·²=6 D be a basis of M2x2 (R).
Suppose that T: M₂×2 (R) → P₂(R) is a linear transformation, such that T(ß₁) = x²,T(ß₂) = 1 +
x, T (B3) = 2 + x − x²,T(B₁) = −1+x.
(a) Find a matrix Z € M3×4 (R), such that if y = Σ½-₁ a¿ß¡, then T(y) = Σ²-o b₁x¹, for some b¡ E
[αί
R, which satisfies b₁ = Z
(b) Find T ([a b]).
C
a2
a 3
a4
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