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consider the system of linear equatio...

consider the system of linear equations
`x_(1)+2x_(2)+x_(3)=3`
`2x_(1)+3x_(2)+x_(3)=3,`
`3x_(1)+5x_(2)+2x_(3)=1`
the system has

A

a unique solution

B

no solution

C

infinite number of solutions

D

exactly three solution

Text Solution

Verified by Experts

The correct Answer is:
B
We, have
`D = |(1,2,1),(2,3,1),(3,5,2)| = 0 and D_(1) = |(3,2,1),(3,3,1),(1,5,2)| != 0` So, the given system of equations has no solution
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Section I - Solved Mcqs
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  2. Evaluate: =|(10 !, 11 !, 12 !), (11 !, 12 !, 13 !), (12 !, 13 !, 14 !)...

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  4. If |p b c a q c a b r|=0 , find the value of p/(p-a)+q/(q-b)+r/(r-c),\...

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  5. If a=1+2+4+… up to n terms b=1+3+9+… up to n terms and c=1+5+25+…....

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  6. If D(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)|,...

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  7. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  8. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1, x+y+al...

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  9. Let a,b,c be such that b(a+c) ne 0. If |{:(a,a+1,a-1),(-b,b+1,b-1)...

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  10. If 3^n is a factor of the determinant |{:(1,1,1),(.^nC1,.^(n+3)C1,.^(n...

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  11. The number of 3 x 3 non-singular matrices, with four entries as 1 and ...

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  12. consider the system of linear equations x(1)+2x(2)+x(3)=3 2x(1)...

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  13. If f(theta) = |(1,tan theta,1),(- tan theta,1,tan theta),(-1,-tan thet...

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  14. If a, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(...

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  15. In a Delta ABC " if " |(1,a,b),(1,c,a),(1,b,c)| =0, then sin^(2) A + s...

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  16. Which of the following values of alpha satisfying the equation |(1+alp...

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  17. The set of all values of lambda for which the system of linear equ...

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  18. If a^(2)+b^(2)+c^(2)+ab+bc+ca le 0 AA a,b,c in R, then value of the de...

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  19. For all values of theta in(0,pi/2), the determinant of the matrix [(...

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  20. The total number of distinct x in R for which |{:(x,,x^(2),,...

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