2. Let L: F3 → F³ be the linear map given by L(x, y, z) = (25x – 4y – 51z, 80x – 1ly – 240z, 82). %3D (a) Find the matrix of L with respect to the standard basis of F3. 1 (b) Find a basis F3 so that the matrix associated to L with respect to this basis is a diagonal matrix.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. Let L: F3 → F³ be the linear map given by
L(x, y, z) = (25x – 4y – 51z, 80x – 1ly – 240z, 82).
%3D
(a) Find the matrix of L with respect to the standard basis of F3.
1
(b) Find a basis F3 so that the matrix associated to L with respect to
this basis is a diagonal matrix.
Transcribed Image Text:2. Let L: F3 → F³ be the linear map given by L(x, y, z) = (25x – 4y – 51z, 80x – 1ly – 240z, 82). %3D (a) Find the matrix of L with respect to the standard basis of F3. 1 (b) Find a basis F3 so that the matrix associated to L with respect to this basis is a diagonal matrix.
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