- point matrix coordinate matrix 3.117 For each of the following ordered bases B for R', (i) find Pg and CB, (ii) find the B coordinate vector for X = [1, 2, 3]', and (iii) check your answer to (ii) by showing that your coordinates do express X as a linear combination of the basis elements. (a) B= {[1,1, 1]', [0, 1, 1]', [0, 0, 1]} (b) / B= {[1,-2, 1]', [2,3, 21', [1, 1,01'} (c) B= {[1,3,2]j, [-1, 1, –1]', [5, 1, -4]'} (d) B= {[1,0, 1]', [1,2, 3]', [1, 1, 1]'}

- point matrix coordinate matrix 3.117 For each of the following ordered bases B for R', (i) find Pg and CB, (ii) find the B coordinate vector for X = [1, 2, 3]', and (iii) check your answer to (ii) by showing that your coordinates do express X as a linear combination of the basis elements. (a) B= {[1,1, 1]', [0, 1, 1]', [0, 0, 1]} (b) / B= {[1,-2, 1]', [2,3, 21', [1, 1,01'} (c) B= {[1,3,2]j, [-1, 1, –1]', [5, 1, -4]'} (d) B= {[1,0, 1]', [1,2, 3]', [1, 1, 1]'}

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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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

3.117(c)
P - point matrix
C - coordinate matrix
3.117 For each of the following ordered bases B for R', (i) find Pg and Cg, (ii)
find the B coordinate vector for X = [1,2, 3]', and (iii) check your answer to
(ii) by showing that your coordinates do express X as a linear combination
of the basis elements.
(a) B= {[1,1, 1J', [0, 1, 1]', [0, 0, 1]}
(b) / B= {[1,–2, 1]', [2, 3, 2]', [1, 1,0]' }
(c) B= {[1,3,2]', [-1, 1, – 1)', [5, 1, –4]'}
(d) B= {[1,0, 1]', [1,2, 3]', [1, 1, 1]'}

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