Consider the system of linear equations
,`a_(1)x+b_(1)y+c_(1)z+d_(1)=0`,
`a_(2)x+b_(2)y+c_(2)z+d_(2)=0`
,`a_(3)x+b_(3)y+c_(3)2+d_(3)=0`
Let us denote by `Delta(a,b,c)` the determinant `|[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(2),c_(3)]|` if `Delta(a,b,c)!=0,` then the value of x in the unique solution of the above equations is

Consider the system of linear equations a_(1)x+b_(1)y+ c_(1)z+d_(1)=0 , a_(2)x+b_(2)y+ c_(2)z+d_(2)= 0 , a_(3)x+b_(3)y +c_(3)z+d_(3)=0 , Let us denote by Delta (a,b,c) the determinant |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| , if Delta (a,b,c) # 0, then the value of x in the unique solution of the above equations is

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

Consider the system of equations a_(1) x + b_(1) y + c_(1) z = 0 a_(2) x + b_(2) y + c_(2) z = 0 a_(3) x + b_(3) y + c_(3) z = 0 If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =0 , then the system has

If Delta is the value of the determinant |(a_(1), b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| then what is the value of the following determinant? |(pa_(1), b_(1), qc_(1)),(pa_(2), b_(2), qc_(2)),(pa_(3), b_(3),qc_(3))| (p ne 0 or 1, q ne 0 or 1)

If the system of equations a_(1)x+b_(1)y+c_(1),a_(2)x+b_(2)y+c_(2)=0 is inconsistent,(a_(1))/(a_(2))=(b_(1))/(b_(2))!=(c_(1))/(c_(2))

Cosnsider the system of equation a_(1)x+b_(1)y+c_(1)z=0, a_(2)x+b_(2)y+c_(2)z=0, a_(3)x+b_(3)y+c_(3)z=0 if |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=0 , then the system has

Show that |[a_(1),b_(1),-c_(1)],[-a_(2),-b_(2),c_(2)],[a_(3),b_(3),-c_(3)]|=|[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(3),c_(3)]|

Suppose the system of equations a_(1)x+b_(1)y+c_(1)z=d_(1) a_(2)x+b_(2)y+c_(2)z=d_(2) a_(3)x+b_(3)y+c_(3)z=d_(3) has a unique solution (x_(0),y_(0),z_(0)) . If x_(0) = 0 , then which one of the following is correct ?