How do I determine whether a system of 3 linear equations is consistent or not?

First, form the system into a 3x3 matrix using the coefficients. Find the determinant of this matrix.If the determinant =/= 0, then the matrix is singular and has a unique solution. The system is consistent and the planes coincide at a point.
If the determinant is 0, then the matrix is non-singular, so use simultaneous equations to attempt to solve the system:
If the system contains 3 equations that are multiples of each other, then the system is consistent and represent a single plane.
If the resolved system gives a redundant equation after elimination/substitution, then the system is consistent and represents a sheaf. The planes coincide at a line.
In all cases where the system is consistent, the system can be resolved to give a set of solutions, whether that be a single point, a line or a plane.

Answered by Further Mathematics tutor

17081 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Differentiate arcsin(2x) using the fact that 2x=sin(y)


Find the area of the surface generated when the curve with equation y=cosh(x) is rotated through 2 pi radians about the x axis, with 2<=x<=6


Integrate the function f(x) = x ln (x) over the interval [1,e].


How can the integrating factor method be derived to give a solution to a differential equation?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences