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'3 (1)-(-). 2 3. Show that the vectors 1 4 2 and −3 are linearly independent. -5

'3 (1)-(-). 2 3. Show that the vectors 1 4 2 and −3 are linearly independent. -5

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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let A=1 B=2 and C=9

(i) Show that the vectors 1 4 Ⓒ) () and (*). a (ii) Let a, b and c be the first three digits of your code number. Express the vector bas a linear 18- combination of the three vectors in (i). X 2 and 3 are linearly independent. (iii) Let a, b and c be the first three digits of your code number, as in (ii). For each of the following maps, state whether or not they are linear transformations. If so, give a matrix for them, and give their image, rank, kernel and nullity. f: y Z ay bz ay+bz X x + a gy→y+b N z+c h: X N ax → by CZ (iv) State the rank-nullity theorem and verify that it is true for those maps in (iii) that are linear transformations.
Transcribed Image Text:(i) Show that the vectors 1 4 Ⓒ) () and (*). a (ii) Let a, b and c be the first three digits of your code number. Express the vector bas a linear 18- combination of the three vectors in (i). X 2 and 3 are linearly independent. (iii) Let a, b and c be the first three digits of your code number, as in (ii). For each of the following maps, state whether or not they are linear transformations. If so, give a matrix for them, and give their image, rank, kernel and nullity. f: y Z ay bz ay+bz X x + a gy→y+b N z+c h: X N ax → by CZ (iv) State the rank-nullity theorem and verify that it is true for those maps in (iii) that are linear transformations.
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