Let T: P₂ P₂ be a mapping defined by T(a + a₁x + a₂x²) = ao + a₁ (x + 1) + a₂(x + 1)². a) Determine whether T is linear or not. b) Find the nullity and rank of T. TDD ha R. dof d]) - d

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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For a,proof using the addition and scalar multiplication property. 

Let T: P₂ P₂ be a mapping defined by
-
T(a + a₁x + a₂x²) = a + a₁ (x+1)+ a₂(x + 1)².
(a) Determine whether T is linear or not.
(b) Find the nullity and rank of T.
Transcribed Image Text:Let T: P₂ P₂ be a mapping defined by - T(a + a₁x + a₂x²) = a + a₁ (x+1)+ a₂(x + 1)². (a) Determine whether T is linear or not. (b) Find the nullity and rank of T.
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