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|[1,bc,bc(b+c)],[1,ca,ca(c+a)],[1,ab,ab(...

`|[1,bc,bc(b+c)],[1,ca,ca(c+a)],[1,ab,ab(a+b)]|=0`

A

0

B

abc

C

ab + bc + ca

D

abc (a + b + c)

Text Solution

Verified by Experts

The correct Answer is:
A
`|(1,bc,a(b+c)),(a,ac,b(c+a)),(1,ab,c(a+b))|`
Applying `C_(3)rarrC_(2)+C_(3)`
`=(ab+bc+ac)|(a,bc,1),(1,ac,1),(1,ab,1)|`
`=(ab+bc+ac)xx0=0`
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NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. If 2A=({:(2,1),(3,2):}), then what is A^(-1) equal to ?

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  2. If ({:(2,3),(4,1):})xx({:(5,-2),(-3,1):})=({:(1,-1),(17,lambda):}), th...

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  3. |[1,bc,bc(b+c)],[1,ca,ca(c+a)],[1,ab,ab(a+b)]|=0

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  4. Consider the following statements in respect of the matrix A=[{:(0,1,2...

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  5. Consider two matrices A=[{:(1,2),(2,1),(1,1):}]and B=[{:(1,2,-4),(2,1,...

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  6. One of the roots of |{:(x+a," "b," "c),(" "a,x+b," "c),(" "a," "b,x+c)...

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  7. If A is any matrix, then the product AA is defined only when A is a ma...

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  8. If A is a skew-symmetric matrix of odd order n , then |A|=0

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  9. If any two adjacent rows or columns of a determinant are intercharged ...

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  10. If a ne b ne c are all positive, then the value of the determinant |{:...

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  11. Let A and B be two matrices such that AB = A and BA = B. Which of the ...

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  12. |{:("6i " "-3i " "1" ),("4 " " 3i" " -1"),("20 " "3 " " i"):}|=x+iy th...

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  13. If the matrix A is such that ({:(1,3),(0,1):})A=({:(1,1),(0,-1):}), t...

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  14. Consider the following statements : 1. Determinant is a square matri...

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  15. If A is an invertible matrix of order 2, then det (A^(-1))is equal to...

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  16. From the matrix equation AB = AC we can conclude B = C provided that

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  17. If {:A=[(4,x+2),(2x-3,x+1)]:} is symmetric, then x =

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  18. If |{:(a,b,0),(0,a,b),(b,0,a):}|=0, then which one of the following is...

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  19. If A and B are square matrices of order 3 such that absA=-1,absB=3," t...

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  20. Which one of the following matrices is an elementary matrix ?

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