use the matrix method to examine the following system of equations for consistency or inconsistency: 2x-y+3z=5, 3x+2y-z=7, 4x+5y-5z=9

A given system of equation is said to be consistent if it has one or more solutions whereas a given system of equation is said to be inconsistent if it has no solutions.
Case -1:
When |A| ≠ 0 , then the given system is consistent and it has a unique solution.
Case-2:
When |A| = 0 and (adj A)B ≠ 0, then the given system is inconsistent and it has a no solution.
Case-3:
When |A| = 0 and (adj A)B = 0, then the given system is consistent and it has infinite solution.

The given system of equations is 2x-y+3z=5, 3x+2y-z=7 and 4x+5y-5z=9.

A=2-1332-145-5, B=579A=2-1332-145-5=2-10+5+1-15+4+315-8=0Thus, the given system of equations is either consistent with infinite solution or inconsistent accordingly adjAB=O or adjABO.C11=-5, C12=11, C13=7C21=10, C22=-22, C23=-14C31=-5, C32=11, C33=7adjA=-511710-22-14-5117T=-510-511-22117-147adjAB=-510-511-22117-147579=-25+70-4555-154+9935-98+63=000=OThus, the given system of equations is consistent with infinitely many solutions.

  • 11
What are you looking for?