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22. Use a determinant to find an equation of the line that passes through the center of the circle (x+3)^2+(y-2)^2=7 and the point (1,4).
\n" ); document.write( "COMPARING WITH STANDARD EQN. OF A CIRCLE
\n" ); document.write( "(X-H)^2+(Y-K)^2=R^2
\n" ); document.write( ",CENTRE IS (H,K)....THAT IS (-3,2)...(X1,Y1)
\n" ); document.write( "LINE JOINING THIS WITH (1,4).....(X2,Y2) IS..(Y-Y1)/(Y2-Y1)=(X-X1)/(X2-X1)
\n" ); document.write( "(Y-4)/(4-2)=(X-1)/(1+3)
\n" ); document.write( "(Y-4)4=2(X-1)
\n" ); document.write( "2Y-8=X-1
\n" ); document.write( "2Y-X-7=0\r
\n" ); document.write( "\n" ); document.write( "-----------------------------------------------------------------------------
\n" ); document.write( "15. Use the inverse matrix method to solve the system of linear equations.
\n" ); document.write( "6x-6y-5z=11
\n" ); document.write( "3x+6y-z=6
\n" ); document.write( "9x-3y+z=0
\n" ); document.write( "SEE THE FOLLOWING EXAMPLE AND TRY .IF STILL IN DIFFICULTY PLEASE COME BACK
\n" ); document.write( "This is a systems of equations problem and I need to
\n" ); document.write( "solve for x,y,z. I do not how to get any of the
\n" ); document.write( "variables or what steps to take to get the answers.
\n" ); document.write( "The problem:
\n" ); document.write( "2x-5y+ ___=-22
\n" ); document.write( "__+y+3z=10
\n" ); document.write( "x+___+8z=15
\n" ); document.write( "The underscores represents blanks or O
\n" ); document.write( "If this had to be an augmented matrix, how would I do
\n" ); document.write( "that and get those variables?
\n" ); document.write( "1 solutions
\n" ); document.write( "Answer 20202 by venugopalramana(1462) About Me on
\n" ); document.write( "2006-04-16 22:01:33 (Show Source):
\n" ); document.write( "2x-5y+ ___=-22...........................I
\n" ); document.write( "__+y+3z=10.....................II
\n" ); document.write( "x+___+8z=15...........................III
\n" ); document.write( "2*EQN.III-EQN.I
\n" ); document.write( "2X+16Z-2X+5Y=30+22=52
\n" ); document.write( "5Y+16Z=52...........................IV
\n" ); document.write( "EQN.IV-5*EQN.II
\n" ); document.write( "5Y+16Z-5Y-15Z=52-50=2
\n" ); document.write( "Z=2....SUBSTITUTING IN EQN.III
\n" ); document.write( "X+8*2=15
\n" ); document.write( "X=15-16=-1
\n" ); document.write( "SUBSTITUTING FOR Z IN EQN.II
\n" ); document.write( "Y+3*2=10
\n" ); document.write( "Y=10-6=4
\n" ); document.write( "USING MATRIX METHOD...AUGMENTED MATRIX IS
\n" ); document.write( "2 -5 0 -22 1 0 0 ?
\n" ); document.write( "0 1 3 10 0 1 0 ?
\n" ); document.write( "1 0 8 15 0 0 1 ?
\n" ); document.write( "NR1=R1/2
\n" ); document.write( "1 -2.5 0 -11
\n" ); document.write( "0 1 3 10
\n" ); document.write( "1 0 8 15
\n" ); document.write( "NR3=R3-R1
\n" ); document.write( "1 -2.5 0 -11
\n" ); document.write( "0 1 3 10
\n" ); document.write( "0 2.5 8 26
\n" ); document.write( "NR3=R3-2.5*R2
\n" ); document.write( "1 -2.5 0 -11
\n" ); document.write( "0 1 3 10
\n" ); document.write( "0 0 0.5 1
\n" ); document.write( "NR3=R3/0.5
\n" ); document.write( "1 -2.5 0 -11
\n" ); document.write( "0 1 3 10
\n" ); document.write( "0 0 1 2
\n" ); document.write( "NR2=R2-3R3
\n" ); document.write( "1 -2.5 0 -11
\n" ); document.write( "0 1 0 4
\n" ); document.write( "0 0 1 2
\n" ); document.write( "NR1=R1+2.5R2
\n" ); document.write( "1 0 0 -1
\n" ); document.write( "0 1 0 4
\n" ); document.write( "0 0 1 2
\n" ); document.write( "HENCE
\n" ); document.write( "X=-1
\n" ); document.write( "Y=4
\n" ); document.write( "Z=2 \n" ); document.write( "