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If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x...

If `f(x)`=`|(a_1+x, b_1+x, c_1+x), (a_2+x, b_2+x, c_2+x),(a_3+x, b_3+x, c_3+x)|`, show that `f''(x)=0` and that`f(x)=f(0)+S ` ,where `S` denotes the sum of all the cofactors of all the element in `f(0)dot`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If |[a^2+lambda^2,ab+clambda,ca-blambda],[ab-clambda,b^2+lambda^2,bc+a...

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  2. Value of |{:(1+x(1),,1+x(1)x,,1+x(1)x^(2)),(1+x(2),,1+x(2)x,,1+x(2)x^(...

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  3. 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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  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. Prove that the value of each the following determinants is zero: |a...

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  6. If l1^2+m1^2+n1^2=1 etc., and l1 l2+m1 m2+n1 n2 = 0, etc. and Delta...

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  8. The value of determinant |[ ^n C(r-1), ^n Cr, (r+1)^(n+2)C(r+1)],[ ^n...

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  9. Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot Then the va...

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  10. If the determinant |[b-c,c-a, a-b],[b^(prime)-c ', c^(prime)-a ', a^(p...

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  11. Let a ,b , c be the real numbers. The following system of equations in...

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  12. By using properties of determinats. Prove that- |(sintheta,costheta,...

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  13. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

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  14. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

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

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  17. 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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  18. If (x)=|(alpha+x,theta+x,lambda+x),(beta+x,varphi+x,mu+x),(gamma+x,psi...

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

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

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