Given the following system of equations a. b. c. x₁ + 2x₂ - 4x3 - X4 + X5 = 7 -X1 + 10x3 3x44x5=-16 2x₁ + 5x₂5x3-4x4- X5 = 2 4x₁ +11x₂-7x3 - 10x4 -2x5= 7 Represent the above system in matrix form Ax=b and use it to verify that the system is consistent and has an infinite number of solutions Calculate the column nullity of the A matrix Determine a particular solution for the system

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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7.
Given the following system of equations
X4 + x5 = 7
3x4 – 4x5
х, + 2 х2 — 4хз
-x1
+ 10x3
= -16
2x, + 5 х, — 5хз - 4x4 — X, %3 2
4x, + 11 х2 — 7хз- 10х, - 2х5 %3 7
Represent the above system in matrix form Ax = b and use it to verify that the system is consistent and
а.
has an infinite number of solutions
b.
Calculate the column nullity of the A matrix
Determine a particular solution for the system
Find a basis for N(A)
с.
d.
е.
Determine a general solution for the system using the particular solution in c) and the basis in d).
Transcribed Image Text:7. Given the following system of equations X4 + x5 = 7 3x4 – 4x5 х, + 2 х2 — 4хз -x1 + 10x3 = -16 2x, + 5 х, — 5хз - 4x4 — X, %3 2 4x, + 11 х2 — 7хз- 10х, - 2х5 %3 7 Represent the above system in matrix form Ax = b and use it to verify that the system is consistent and а. has an infinite number of solutions b. Calculate the column nullity of the A matrix Determine a particular solution for the system Find a basis for N(A) с. d. е. Determine a general solution for the system using the particular solution in c) and the basis in d).
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