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Prove that |[a x-b y-c z, a y+b x, c x+...

Prove that `|[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot`

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B...

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  2. Let lambdaa n dalpha be real. Find the set of all values of lambda for...

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  3. Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b...

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  4. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

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  5. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

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  6. If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],...

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  7. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

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  8. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

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  9. Find the value of lambda for which |{:(2a1+b1 , 2a2+b2 , 2a3+b3),(2b1+...

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  10. Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c...

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  11. if a determinant of order 3xx 3 is formed by using the numbers 1 ...

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  12. If z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz is (a) p...

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  13. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

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  14. Let omega be the complex number cos((2pi)/3)+isin((2pi)/3). Then the...

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  15. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

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  16. Consider the determinant Delta=|[a1+b1x^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...

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  17. If a x1^2+b y1^2+c z1^2=a x2 ^2+b y2 ^2+c z2 ^2=a x3 ^2+b y3 ^2+c z3 ^...

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  18. If A , B ,a n dC are the angles of triangle, show that the system of...

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  19. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

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  20. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|[a1,a2,a3],[5, 4,a6...

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