SOLUTION: Solve the following systems using inverse matrices. can you also show me the steps.. thanks
2x - y = 2
2x - 2y = 4
2x + 3y + 4z = 3
-13x + 5y - 2z = 3
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Question 176635: Solve the following systems using inverse matrices. can you also show me the steps.. thanks
2x - y = 2
2x - 2y = 4
2x + 3y + 4z = 3
-13x + 5y - 2z = 3
-3x + 4y + 3z = 6
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
2x - y = 2
2x - 2y = 4
:
matrix A =
matrix C =
adj A= the adjunct of a 2x2 matrix is the matrix in which the main diagonal elements are switched and the other elements are multiplied by -1.
:
the inverse of A or is
:
so det A=-2(2)-2(-1)=-2--->-1/2
=(1/det A)(adj A)=-1/2=
:
now finally the answer is found by multiplying the inverse of A by matrix Cmat C
:
=
:
so x=0 and y=-2
::
::
::
::
2x + 3y + 4z = 3
-13x + 5y - 2z = 3
-3x + 4y + 3z = 6
:
RHS is the numbers on the right hand side of the equation.
C1 is column 1...etc
R1 is row 1...etc
:Matrix A
:
det A is the determinant of A
:
det A=(2) det-(-13)det+(-3)det=46-91+78=33
:
det A=13
:
matrix A(C1 replaced with RHS) lets call A1
A1=
det A1=b>(3) det-(3)det+(6)det=69+21-156=-66
:
matrix A(C2 replaced with RHS) lets call A2
A2=
det A2=b>(2) det-(-13)det+(-3)det=42-195+54=-99
:
matrix A(C3 replaced with RHS) lets call A3
A3=
det A3=b>(2) det-(-13)det+(-3)det=36+78+18=132
:
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