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4.2.6. Find an orthonormal basis for the following subspaces of R*: (a) the span of the vectors 0·0 ; (b) the kernel of the matrix =1); (c) the coimage 2 1 0 3 2 -1 -2 1 2-4 of the preceding matrix; (d) the image of the matrix 0 0 -2 4 5 of the preceding matrix; (f) the set of all vectors orthogonal to (1, 1, −1, −1)ª. 2 1 -1 (e) the cokernel

4.2.6. Find an orthonormal basis for the following subspaces of R*: (a) the span of the vectors 0·0 ; (b) the kernel of the matrix =1); (c) the coimage 2 1 0 3 2 -1 -2 1 2-4 of the preceding matrix; (d) the image of the matrix 0 0 -2 4 5 of the preceding matrix; (f) the set of all vectors orthogonal to (1, 1, −1, −1)ª. 2 1 -1 (e) the cokernel

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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4.2.6. Find an orthonormal basis for the following subspaces of R¹: (a) the span of the vectors -1 000 (b) the kernel of the matrix 1 1 1 -2 2 -4 of the preceding matrix; (d) the image of the matrix 0 0 -2 4 5 of the preceding matrix; (f) the set of all vectors orthogonal to (1, 1, —1,−1)ª. -1 2 2 1 23 1 2 0 -1 2 1 1 }); ; (c) the coimage ; (e) the cokernel
Transcribed Image Text:4.2.6. Find an orthonormal basis for the following subspaces of R¹: (a) the span of the vectors -1 000 (b) the kernel of the matrix 1 1 1 -2 2 -4 of the preceding matrix; (d) the image of the matrix 0 0 -2 4 5 of the preceding matrix; (f) the set of all vectors orthogonal to (1, 1, —1,−1)ª. -1 2 2 1 23 1 2 0 -1 2 1 1 }); ; (c) the coimage ; (e) the cokernel
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