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Prove tha following |{:(a+b+nc,na-a,nb...

Prove tha following
`|{:(a+b+nc,na-a,nb-b),(nc-c,b+c+na,nb-b),(nc-c,na-a,c+a+nb):}|=n(a+b+c)^(3)`.

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MODERN PUBLICATION-DETERMINANTS-Revision Exercise
  1. For the matrix A=[{:(3,1),(7,5):}]. Find 'x' and 'y' so that A^(2)+xI=...

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  2. |(1,cos(beta-alpha),cos(gamma-alpha)), (cos(alpha-beta),1,cos(gamma-be...

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  3. Prove tha following |{:(a+b+nc,na-a,nb-b),(nc-c,b+c+na,nb-b),(nc-c,n...

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  4. Prove: |(a^2+b^2)/ccc a(b^2+c^2)/a a bb(c^2+a^2)/b|=4a b c

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  5. Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(...

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  6. Show that | (-a(b^2 + c^2 - a^2), 2b^3, 2c^3), (2a^3, -b(c^2 + a...

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  7. Prove that Delta=|(1,bc+ad,b^(2)c^(2)+a^(2)d^(2)),(1,ca+bd,c^(2)a^(2)+...

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  8. |[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3)(a+4),a+4,1]|=-2

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  9. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

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  10. Prove that Delta=[a+b x c+dx p+q x a x+b c x+d p x+q u v w]=(1-x^2)|a ...

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  11. Ecaluate [{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,co...

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  12. If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+...

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  13. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

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  14. If a,b,c are in A.P. find the value of: ||2y+4, 5y+7, 8y+a],[3y+5, 6y+...

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  15. If ax^(2)+2hxy+by^(2)+2gx+2fy+c-=(lx+my+n)(l'x+m'y+n'), then prove tha...

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  16. If a+b+c=0 and |[a-x,c,b],[c,b-x,a],[b,a,c-x]|=0 then x=

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  17. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

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  18. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

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  19. If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

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  20. If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}], then show that A^(3)=A^(-1).

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