Determining whether system of equations have a solution

Thread starter katerine
Start date Jan 19, 2011
Tags

System System of equations

AI Thread Summary

To determine the value of 'a' in the given linear system of equations, one must analyze the coefficients and constants to identify conditions for different types of solutions. For no solution, the equations must be inconsistent, which can occur if the ratios of the coefficients are equal but the constants differ. A unique solution arises when the system is consistent and the equations are independent, typically when the determinant of the coefficient matrix is non-zero. Infinitely many solutions occur when the equations are dependent, meaning they represent the same plane in three-dimensional space. The discussion emphasizes understanding the relationships between the equations to classify the solutions effectively.

Jan 19, 2011

katerine

how know how to do tis question
determine the value a
for which the resulting linear system has
i) no solution
ii)a unique solution
iii)infinitely many solution

x+y+z=3
x+2y+z=3
x+y+(a^2-8)z=a

Physics news on Phys.org

Jan 19, 2011

Fredrik

Staff Emeritus

Science Advisor

Homework Helper

Insights Author

Gold Member

katerine said:

x+y+z=3
x+2y+z=3

What do these two equations tell you about x,y and z?

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

View full post »