Find the matrix of the given linear transformation T with respect to the given basis. Determine whether T is an isomorphism. If I isn't an isomorphism, find bases of the kernel and image of T, and thus determine the rank of T. [1 2] [1-6] For the space of U²×² of upper triangular 2 × 2 matrices, use the basis [10] 1.61 T (M) = M В = " M from U2x2 to U²×2

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find the matrix of the given linear transformation T with respect to the given basis. Determine whether
T is an isomorphism. If I isn't an isomorphism, find bases of the kernel and image of T, and thus
determine the rank of T.
T (M)
= M
[1 2] [1 2]
61-63
0
For the space of U²×2
M from U²x2 to U²×2
of upper triangular 2 x 2 matrices, use the basis
[1 0] [0 1] 01
8 = (61-81·61)
Transcribed Image Text:Find the matrix of the given linear transformation T with respect to the given basis. Determine whether T is an isomorphism. If I isn't an isomorphism, find bases of the kernel and image of T, and thus determine the rank of T. T (M) = M [1 2] [1 2] 61-63 0 For the space of U²×2 M from U²x2 to U²×2 of upper triangular 2 x 2 matrices, use the basis [1 0] [0 1] 01 8 = (61-81·61)
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