b) Consider the following system of linear equations: 2x1 + 2x3 - 3x3 =-1 3x1 - X2 +2x3 =7 5x1 + 3x2 - 4x3 = 2 i) Express this system of linear equations with a single function f: R - R, without using a matrix. i) Using the fact that -1 2 -3 3 -1 2 =|-11 3 -4 -7 -2 4 calculate the solution to the system of linear equations above. Show your working. iii) Using the fact that 1 2 -3 det 3 -1 2=0 15 3 -4 explain why we can't use the same method as before to find solutions to the system of linear equations below: *1 + 2x3 - 3x3 = 0 3x1 - Xạ + 2x, m 0 5x1 + 3x2 - 4x, = 0 iv) For the purposes of this question, we will call a system of linear equations uniform when all the constants are zero. For example, the system in the previous part is uniform. Explain why we can always find at least one solution for any uniform system of linear equations.
b) Consider the following system of linear equations: 2x1 + 2x3 - 3x3 =-1 3x1 - X2 +2x3 =7 5x1 + 3x2 - 4x3 = 2 i) Express this system of linear equations with a single function f: R - R, without using a matrix. i) Using the fact that -1 2 -3 3 -1 2 =|-11 3 -4 -7 -2 4 calculate the solution to the system of linear equations above. Show your working. iii) Using the fact that 1 2 -3 det 3 -1 2=0 15 3 -4 explain why we can't use the same method as before to find solutions to the system of linear equations below: *1 + 2x3 - 3x3 = 0 3x1 - Xạ + 2x, m 0 5x1 + 3x2 - 4x, = 0 iv) For the purposes of this question, we will call a system of linear equations uniform when all the constants are zero. For example, the system in the previous part is uniform. Explain why we can always find at least one solution for any uniform system of linear equations.
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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Transcribed Image Text:b) Consider the following system of linear equations:
2x1 + 2x3 - 3x3 = -1
3x1 - x2 + 2x3 =7
5x1 + 3x2 - 4x3 = 2
i) Express this system of linear equations with a single function f: R- R', without
using a matrix.
i) Using the fact that
-1
2
-3
3 -1
2
=|-11
3
-4
-7
-2
4
calculate the solution to the system of linear equations above. Show your working.
iii) Using the fact that
1
2
-3
det 3 -1
2
= 0
15
3
-4
explain why we can't use the same method as before to find solutions to the system
of linear equations below:
*1 + 2x3 - 3x3 = 0
3x1 - Xạ + 2x m 0
5x1 + 3x2 - 4x, = 0
iv) For the purposes of this question, we will call a system of linear equations uniform
when all the constants are zero. For example, the system in the previous part is
uniform. Explain why we can always find at least one solution for any uniform
system of linear equations.
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