Consider the linear transformation T: R → R whose matrix A relative to the standard basis is given. 3 1 A 4= [-28] (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) ( (21, 2₂) (b) Find a basis for each of the corresponding eigenspaces. B₁ = B₂ = = A' = (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the linear transformation T: R → Rn whose matrix A relative to the standard basis is given.
3 1
-[-28]
6
A =
(a) Find the eigenvalues of A. (Enter your answers from smallest to largest.)
(1₁, 1₂) = ( [
(b) Find a basis for each of the corresponding eigenspaces.
B₁ =
B₂ =
{
(c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b).
A' =
Transcribed Image Text:Consider the linear transformation T: R → Rn whose matrix A relative to the standard basis is given. 3 1 -[-28] 6 A = (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (1₁, 1₂) = ( [ (b) Find a basis for each of the corresponding eigenspaces. B₁ = B₂ = { (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b). A' =
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