24th 24 Solve the following system of equations by matrix method, when x ≠ 0, y - Maths - Matrices

Question

24th

24     S o l v e   t h e   f o l l o w i n g
  s y s t e m   o f   e q u a t i o n s   b y
  m a t r i x   m e t h o d ,   w h e n   x
  ≠   0 ,   y   ≠   0   a
n d   z   ≠   0        
      2 x - 3 y + 3 z = 10 ,   1 x + 1 y + 1 z
= 10           a n d   3 x - 1 y + 2
z = 13

Aarushi Mishra · Accepted Answer

2x-3y+3z=101x+1y+1z=103x-1y+2z=13Letp=1xq=1yr=1zThen equation become2p-3q+3r=10p+q+r=103p-q+2r=13We will be solving these systems of equationsAX=BA-1AX=A-1BIX=A-1BX=A-1BConstruct coefficent matrixA=2-331113-12detA=2-331113-12=3-5-7=-9X=pqrB=101013Now finding A-1Cofactor matrix C=c11c12c13c21c22c23c31c32c33c11=3c12=1c13=-4c21=3c22=-5c23=-7c31=-6c32=1c33=5C=31-43-5-7-615Adj A=CT=33-61-51-4-75A-1=1detAAdj A=-1933-61-51-4-75X=A-1B=-1933-61-51-4-75101013=-19-18-27-45=235pqr=235comparingp=21x=2x=12q=31y=3y=13r=51z=5z=15

24th 24 . S o l v e t h e f o l l o w i n g s y s t e m o f e q u a t i o n s b y m a t r i x m e t h o d , w h e n x ≠ 0 , y ≠ 0 a n d z ≠ 0 . 2 x - 3 y + 3 z = 10 , 1 x + 1 y + 1 z = 10 a n d 3 x - 1 y + 2 z = 13

24th

$24 . S o l v e t h e f o l l o w i n g s y s t e m o f e q u a t i o n s b y m a t r i x m e t h o d, w h e n x \neq 0, y \neq 0 a n d z \neq 0 . \frac{2}{x} - \frac{3}{y} + \frac{3}{z} = 10, \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 10 a n d \frac{3}{x} - \frac{1}{y} + \frac{2}{z} = 13$