If `a_1/a_2=b_1/b_2=c_1/c_2` then the solution of the system of equation is .......

If (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2) , then the equations a_1x + b_1y + c_1 =0 and a_2x + b_2y + c_2=0 are _________. (consistent/inconsistent)

|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 then the system of equations a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 has (A) no solution (B) one trivial and one non trivial solutions (C) only the trivial solution (0,0,0) (D) more than two solution

Consider the following system if equations a_1x+b_1y+c_1z=d_1, a_2x+b_2y+c_2z=d_2, a_3x+b_3y+c_3z=d_3 Let /_\= |(a_1,b_1,c_1), (a_2,b_2,c_2), (a_3,b_3,c_3)|, /_\_1= |(d_1,b_1,c_1), (d_2,b_2,c_2), (d_3,b_3,c_3)|, ,/_\_2=|(a_1,d_1,c_1), (a_2,d_2,c_2), (a_3,d_3,c_3)|,, /_\_3=|(a_1,b_1,cd_1), (a_2,b_2,d_2), (a_3,b_3,d_3)|, The given system of equations will have i. unique solution of /_\!=0 ii. infinitely many solutions if /_\=/_\_1=/_\_3=0 . iii. no solution if /_\=0 and any of /_\_1, /_\_2, /_\_3 is none zero. On the basis of above informatioin answer the following questions for the following system of linear equations. 2x+ay+6z=8, x+2y+bz=5, x+y+3z=4 The given system of equatioin has infinitely many solution if (A) a!=2, b!=3 (B) a!=2,b=3 (C) a=2,b epsilonR (D) a!=2, bepsilonR

Consider the following system if equations a_1x+b_1y+c_1z=d_1, a_2x+b_2y+c_2z=d_2, a_3x+b_3y+c_3z=d_3 Let /_\= |(a_1,b_1,c_1), (a_2,b_2,c_2), (a_3,b_3,c_3)|, /_\_1= |(d_1,b_1,c_1), (d_2,b_2,c_2), (d_3,b_3,c_3)|, ,/_\_2=|(a_1,d_1,c_1), (a_2,d_2,c_2), (a_3,d_3,c_3)|,, /_\_3=|(a_1,b_1,cd_1), (a_2,b_2,d_2), (a_3,b_3,d_3)|, The given system of equations will have i. unique solution of /\=0 ii. infinitely many solutions if /_\=/_\_1=/_\_3=0 . iii. no solution if /_\=0 and any of /_\_1, /_\_2, /_\_3 is none zero. On the basis of above informatioin answer thefollowing questions for the following system of linear equations. 2x+ay+6z=8, x+2y+bz=5, x+y+3z=4 The given system of equatioin has unique solution if (A) a=2,b=2 (B) a!=2,b=3 (C) a!=2, b!=3 (D) a=2,b!=3

Consider the following system of equations a_1x+b_1y+c_1z=d_1, a_2x+b_2y+c_2z=d_2, a_3x+b_3y+c_3z=d_3 Let /_\= |(a_1,b_1,c_1), (a_2,b_2,c_2), (a_3,b_3,c_3)|, /_\_1= |(d_1,b_1,c_1), (d_2,b_2,c_2), (d_3,b_3,c_3)|, ,/_\_2=|(a_1,d_1,c_1), (a_2,d_2,c_2), (a_3,d_3,c_3)|,, /_\_3=|(a_1,b_1,cd_1), (a_2,b_2,d_2), (a_3,b_3,d_3)|, The given system of equations will have i. unique solution of /_\!=0 ii. infinitely many solutions if /_\=/_\_1=/_\_3=0 . iii. no solution if /_\=0 and any of /_\_1, /_\_2, /_\_3 is none zero. On the basis of above informatioin answer thefollowing questions for the following system of linear equations. x+y+z=6, x+2y+3z=14, 2x+5y+lamdaz=mu The given system of equations has infinitely many solution if (A) lamda=3, mu=10 (B) lamda!=3, mu=10 (C) lamda=3,mu!=0 (D) lamda!=3, mu!=10

Consider the following system of equations a_1x+b_1y+c_1z=d_1, a_2x+b_2y+c_2z=d_2, a_3x+b_3y+c_3z=d_3 Let /_\= |(a_1,b_1,c_1), (a_2,b_2,c_2), (a_3,b_3,c_3)|, /_\_1= |(d_1,b_1,c_1), (d_2,b_2,c_2), (d_3,b_3,c_3)|, ,/_\_2=|(a_1,d_1,c_1), (a_2,d_2,c_2), (a_3,d_3,c_3)|,, /_\_3=|(a_1,b_1,d_1), (a_2,b_2,d_2), (a_3,b_3,d_3)| , The given system of equations will have i. unique solution of /_\!=0 ii. infinitely many solutions if /_\=/_\_1=/_\_3=0. iii. no solution if /_\=0 and any of /_\_1, /_\_2, /_\_3 is none zero. On the basis of above informatioin answer thefollowing questions for the following system of linear equations. x+y+z=6, x+2y+3z=14, 2x+5y+lamda=mu The given system of equations has no solution if (A) lamda=8, mu=36 (B) lamda!=8, muepsilon R (C) lamda=8, mu!=36 (D) lamda!=8, mu!=36