Home > Algebra calculators > Linear Equation in Two Variables using Inverse Matrix Method calculator

Solve Linear Equation in Two Variables
Polynomial-1
Polynomial-2

Also find solution using other methods

SolutionHelpSubstitution MethodElimination MethodCross Multiplication MethodAddition-Substration MethodInverse Matrix MethodCramer's RuleGraphical Method
 5. Inverse Matrix Method Solve linear equations 12x+5y=7 and x+y=7 using Using Matrix Method=> (12x+5y-7) = 0=> (x+y-7) = 0Here 12x+5y=7, x+y=7Now converting given equations into matrix form [[12,5],[1,1]] [[ x ],[ y ]] = [[7],[7]]Now, A = [[12,5],[1,1]], X = [[ x ],[ y ]] and B = [[7],[7]]:. AX = B:. X = A^-1 B| A |=|[12,5],[1,1]| = 12 × 1 - 5 × 1 = 12 - 5 = 7"Here, " | A | = 7 != 0 :. A^(-1)" is possible."Adj(A)=Adj[[12,5],[1,1]]=[[+(1),-(1)],[-(5),+(12)]]^T=[[1,-1],[-5,12]]^T=[[1,-5],[-1,12]]"Now, "A^(-1)=1/| A | × Adj(A)"Here, "X = A^(-1) × B:. X =1/| A | × Adj(A) × B=1/7 × [[1,-5],[-1,12]] × [[7],[7]] =1/7 ×[[1*7 + -5*7],[-1*7 + 12*7]] =1/7 ×[[-28],[77]] =[[-4],[11]]:.[[ x ],[ y ]] = [[-4],[11]]:. x = -4, y = 11

Copyright © 2016. All rights reserved.
Ad: Web Hosting By Arvixe