If a1x+b1y+c1z=0, a2x+b2y+c2z=0, a3x+b3...

If `a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0` and `|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0` , then the given system has, 1) more than two solutions 2) one trivial and one non trivial solutions 3) no solution 4) only trivial solution (0, 0, 0)

`(Delta(bcd))/(Delta(abc))`

`(Delta(-bcd))/(Delta(abc))`

`(Delta(acd))/(Delta(abc))`

`-(Delta(abd))/(Delta(abc))`

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|(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

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If Delta =|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| then the value of |(2a_1+3b_1+4c_1,b_1,c_1),(2a2+3b_2+4c_2,b_2,c_2),(2a_3+3b_3+4c_3,b_3,c_3)| is equal to

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 if /_\!=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

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If u=a_1x+b_1y+c_1=0,v=a_2x+b_2y+c_2=0, and (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2), then the curve u+k v=0 is (a)the same straight line u (b)different straight line (c)not a straight line (d)none of these

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE

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