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(i) Show that the vectors 4 (1)-(2) and (3) 2 and 3 are linearly independent. a (ii) Let a, b and c be the first three digits of your code number. Express the vector bas a linear combination of the three vectors in (i).

(i) Show that the vectors 4 (1)-(2) and (3) 2 and 3 are linearly independent. a (ii) Let a, b and c be the first three digits of your code number. Express the vector bas a linear combination of the three vectors in (i).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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A=1 B=2 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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