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M2r2 is the vector space consisting of all 2x2 real matrices. The linear transformation T: M2r2 x → M2»2 is defined as [1 1] T(x) = 0 0 x + x 1 a) Find the dimension of T(M22) (the image of T). b) Find a basis for the nullspace of T.

M2r2 is the vector space consisting of all 2x2 real matrices. The linear transformation T: M2r2 x → M2»2 is defined as [1 1] T(x) = 0 0 x + x 1 a) Find the dimension of T(M22) (the image of T). b) Find a basis for the nullspace of T.

Advanced Engineering Mathematics
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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M22 is the vector space consisting of all 2x2 real matrices. The linear transformation T: M2r2 x → M22 is defined as T(x) x + x 0 0 a) Find the dimension of T(M22) (the image of T). b) Find a basis for the nullspace of T.
Transcribed Image Text:M22 is the vector space consisting of all 2x2 real matrices. The linear transformation T: M2r2 x → M22 is defined as T(x) x + x 0 0 a) Find the dimension of T(M22) (the image of T). b) Find a basis for the nullspace of T.
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