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If `a , b , c` are distinct real numbers and the system of equations `a x+a^2y+(a^3+1)z=0` `b x+b^2y+(b^3+1)z=0` `c x+c^2y+(c^3+1)=0` has a non-trivial solution, show that `a b c=-1`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
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  2. If f(x)=|[a,-1 ,0],[ax,a,-1],[a x^2,a x, a]|, using properties of det...

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  3. If a , b , c are distinct real numbers and the system of equations a x...

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  4. If x , y , z are not all zero such that a x+y+z=0, x+b y+z=0, ...

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  5. Find the value of lambda for which the homogeneous system of equations...

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  6. If the system of equations x=c y+b z y=a z+c x z=b x+a y has...

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  7. A matrix A of order 3x3 has determinant 5. What is the value of |3A|?

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  8. If A is a square matrix such that |A|=2 , write the value of |AA^T|

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  9. Find the real values of lambda for which the following system of linea...

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

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  11. Which of the following is not correct in a given determinant of A , wh...

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  12. Let |x2xx^2x6xx6|=a x^4+b x^3+c x^2+dx+edot Then, the value of 5a+4b+3...

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  13. Let delta=|A x x^2 1 B y y^2 1 C z z^2 1|a n d1=|A B C x y z y z z xx ...

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  14. If Delta1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta2=|[q,-b, y],[-p,...

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  15. Without expanding show that: =|(cose c^2theta,cot^2theta,1),(cot^2thet...

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  16. Find the value of the determinant =|(2, 3, 4),( 5, 6, 8),( 6x,9x ,12 x...

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  17. Without expanding evaluate the determinant |[41,1,5],[79,7,9],[29,5,3]...

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  18. Show that |1a bc1b c+a1c a+b|=0

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  19. Without expanding evaluate the determinant |[(a^x+a^(-x))^2,(a^x-a^(-x...

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