AP EAMCET201920 Apr 2019Morning ShiftMathematicsDeterminantsActual
Investigate the values of ( ) and ( ) for the system (x+2 y+3 z=6, x+3 y+5 z=9 ), (2 x+5 y+ z= ) and match the values in List - I with the items in List - II.
Options
- A( array lll A & B & C 1 & 2 & 3 array )
- B( array lll A & B & C 3 & 1 & 2 array )
- C( array lll A & B & C 2 &3 &1 array )
- D( array lll A & B & C 3 &2 &1 array )
Correct answer
B. ( array lll A & B & C 3 & 1 & 2 array )
Step-by-step solution
Given system of linear equations is ( aligned x+2 y+3 z & =6 x+3 y+5 z & =9 and 2 x+5 y+ z & = aligned ) Now, according to Cramer's rule, ( aligned & = | array lll 1 & 2 & 3 1 & 3 & 5 2 & 5 & array |=1(3 -25)-2( -10)+3(5-6) & = -8 & ₁= | array lll 6 & 2 & 3 9 & 3 & 5 & 5 & array |=6(3 -25)-2(9 -5 ) & +3(45-3 )= -15 & ₂= | array lll 1 & 6 & 3 1 & 9 & 5 2 & & array |=1(9 -5 )-6( -10)+3( -18) & =3 -4 +6 aligned ) and ( ₃= | array lll 1 & 2 & 6 1 & 3 & 9 2 & 5 & array |=1(3 -45)-2( -18)+6(5-6) = - 15 ) Now, if ( =8 ) a