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Without expanding a determinant at any stage, show that `abs((x^2+x ,x+1 , x-2),(2x^2+3x-1 ,3x , 3x-3) , (x^2+2x+3, 2x-1 ,2x-1))=xA+B` ,where `A` and `B` are determinant of order 3 not involving `xdot`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. if f(x)=|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)...

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  3. Without expanding a determinant at any stage, show that abs((x^2+x ,x+...

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  4. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

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  5. Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...

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  6. The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)...

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  7. If y=|[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1, 1]| find (dy)/(dx)dot

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  8. Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...

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  9. Consider the system linear equations in x ,y ,a n dz given by (sin3the...

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  10. If alpha,beta "and" gamma are real number without expanding at any sta...

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  11. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

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  12. If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta...

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  13. Prove that |[a1alpha1+b1beta1, a1alpha2+b1beta2, a1alpha3+b1beta3], [a...

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  14. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value o...

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  15. Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) ...

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  16. If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value ...

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  17. If |[x^n, x^(n+2), x^(n+3)], [y^n, y^(n+2), y^(n+3)], [z^n, z^(n+2), z...

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  18. Solve the system of the equations: a x+b y+c z=d, a^2x+b^2y+c^2z=d^2,...

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  19. If |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=0 , then the line a x+b y+c=0...

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  20. If 2a x-2y+3z=0,x+a y+2z=0,a n d, 2x+a z=0 have a nontrivial solutio...

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