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Consider the system of equations a(1) ...

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

A

more than two solutions

B

one trivial and one non-trivial solutions

C

no solution

D

only trivial solution `(0, 0,0)`

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-DETERMINANTS-Chapter Test
  1. Consider the system of equations a(1) x + b(1) y + c(1) z = 0 a(2)...

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  2. If D = |(1,1,1),(1,1 +x,1),(1,1,1 +y)| " for " x!= 0, y != 0, then D i...

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  3. If |(x +a,b,c),(a,x +b,c),(a,b,x +c)| = 0, then x equals

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  4. |(sin^(2) x,cos^(2) x,1),(cos^(2) x,sin^(2) x,1),(- 10,12,2)| =

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  5. The system of linear equations x + y + z = 2 2x + y -z = 3 3x + ...

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  6. The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) the...

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  7. |(bc,bc'+b'c,b'c'),(ca,ca'+c'a,c'a'),(ab,ab'+a'b,a'b')| is equal to

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  8. If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamm...

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  9. One root of the equation |(3x-8, 3, 3),(3,3x-8, 3),(3,3,3x-8)|=0 is

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  10. If a,b,c are non-zero real numbers then D=|[b^2 c^2, bc, b+c] , [c^2a^...

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  11. If x, y , z are in A.P., then the value of the det (A) is , where A ...

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  12. The value of |(b +c,a,a),(b,c +a,b),(c,c,a +b)|, is

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  13. If a , b , c are non-zero real numbers and if the system of equations ...

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  14. If a!=6,b,c satisfy|[a,2b,2c],[3,b,c],[4,a,b]|=0 ,then abc =

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  15. The value of Delta = |(1^(2),2^(2),3^(2)),(2^(2),3^(2),4^(2)),(3^(2),4...

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  16. The value of Delta = |(a,a +b,a +2b),(a +2b,a,a +b),(a +b,a +2b,a)| is...

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  17. If all the elements in a square matrix A of order 3 are equal to 1 or ...

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  18. The roots of the equation |(1,4,20),(1,-2,5),(1,2x,5x^(2))| = 0 are

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  19. If f(x) = |(sin x,cos x,tan x),(x^(3),x^(2),x),(2x,1,1)|, " then " lim...

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  20. If A, B and C are the angles of a triangle and |(1,1,1),(1 + sin A,1...

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