Question 729677
{{{iA+iB+iC=0}}}......1
{{{7iA-5iB =2}}}.......2
{{{5iB-3iC=-1}}}.......3

{{{iA}}}=?,{{{iB}}}=?,{{{iC}}}=?


I am going to find {{{A}}},{{{B}}}, {{{C}}}


start with {{{iA+iB+iC=0}}}......1...solve for {{{A}}}

{{{A=(-iB-iC)/i}}}

{{{A=(-cross(i)B-cross(i)C)/cross(i)

{{{higlight(A=-B-C)}}}......plug it in 2


{{{7i(-B-C)-5iB =2}}}.......2

{{{-7iB-7iC-5iB =2}}}

{{{-12B-7C=2}}}....both side multiply by {{{-1}}}

{{{12B+7C=-2}}}....solve for {{{C}}}

{{{7C =-2-12iB}}}

{{{highlight(C =(-2-12iB)/7)}}}........plug in 3


{{{5iB-3iC=-1}}}.......3

{{{5iB-3i(-2-12iB)/7=-1}}}.......solve for {{{B}}}

{{{5iB-(-6i-12*3i*iB)/7=-1

{{{5iB-(-6i+-36i^2B)/7=-1}}}

{{{5iB-(-6i-36(-1)B)/7=-1}}}

{{{5iB-(-6i+36B)/7=-1}}}.......both sides multiply by {{{7}}}

{{{35iB-(-6i+36B)=-7}}}

{{{35iB+6i-36B=-7}}}

{{{B(35i-36)=-7+6i}}}

{{{highlight(B=(-7+6i)/(35i-36))}}}.........now find C


{{{C =(2+12iB)/7}}}


{{{C =(2+12i(-7+6i)/(35i-36))/7}}}


{{{C =(2+(-7*12i+6i*12i)/(35i-36))/7}}}


{{{C =(2(35i-36)+(-84i+72i^2))/(35i-36))/7}}}


{{{C =(70i-72-84i-72)/(35i-36))/7}}}


{{{highlight(C =(-14i-144)/7(35i-36)))}}}


and now find {{{A}}}

{{{A=(-B-C)}}}

{{{A=(-(-7+6i)/(35i-36))-((-14i-144)/7(35i-36)))}}}


{{{A=(7-6i)/(35i-36)+(14i+144)/7(35i-36)}}}


{{{A=(7(7-6i)+14i+144)/7(35i-36)}}}


{{{A=(49-42i+14i+144)/7(35i-36)}}}


{{{highlight(A=(-28i+193)/7(35i-36))}}}


since you need {{{iA}}},{{{iB}}},{{{iC}}}, your solutions are:

{{{iA=i(-28i+193)/(7(35i-36))}}}

{{{iB=i(-7+6i)/(35i-36)}}} and

{{{iC=i(-14i-144)/(7(35i-36))}}}



check:

{{{iA+iB+iC=0}}}......1

{{{i(-28i+193)/(7(35i-36))+i(-7+6i)/(35i-36)+i(-14i-144)/(7(35i-36))=0}}}......1

{{{(-28i^2+193i)/(7(35i-36))+(-7i+6i^2)/(35i-36)+(-14i^2-144i)/(7(35i-36))=0}}}

{{{(-28(-1)+193i)/(7(35i-36))+(-7i+6(-1))/(35i-36)+(-14(-1)-144i)/(7(35i-36))=0}}}

{{{(28+193i)/(7(35i-36))+(-7i-6)/(35i-36)+(14-144i)/(7(35i-36))=0}}}


{{{(28+193i+7(-7i-6)+14-144i)/(7(35i-36))=0}}}


{{{(28+193i-49i-42+14-144i)=0*(7(35i-36))}}}


{{{28+193i-28-193i=0}}}


{{{28-28+193i-193i=0}}}


{{{0=0}}}