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Let a, b, and c be three real numbers sa...

Let a, b, and c be three real numbers satifying `[(a, b, c)]`
`[(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)]`
If the point P(a, b, c) with reference to (E) lies on the plane `2x+y+z=1`, then the value of `7a+b+c` is

A

0

B

12

C

7

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
`a+ 8b +7c = 0, 9a + 2b 3c=0`
`7a + 7b +7c=0`
Solving these equations, we get
`b=6a`
`rArr c= -7a`
Now, `2x + y + z = 0`
`rArr 2a + 6 a + (-7a) = 1`
`rArr a= 1, b = 6, c=-7`
`therefore 7a + b+ c= + 6 - = 6`
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ARIHANT MATHS ENGLISH-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
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  7. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

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  9. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

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  11. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

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  12. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

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  13. Let P and Q be 3xx3 matrices P ne Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P,...

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  14. IF P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of 3xx3 matrix A and...

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  15. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

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  16. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

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  17. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

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  18. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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  19. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

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