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Factorize the following. [[x+a,b,c],[b,x...

Factorize the following. `[[x+a,b,c],[b,x+c,a],[c,a,x+b]]`

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Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]] =4ab

Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[z,c,r]]=[[x,y,z],[p,q,r],[a,b,c]]

Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =2(b+c)(c+a)(a+b)

Prove that the following. [[a,a^2,a^3],[b,b^2,b^3],[c,c^2,c^3]] = abc(a-b)(b-c)(c-a)

Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]] =(b-c)(c-a)(a-b)

Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] = a^3+b^3+c^3-3abc

Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

MBD PUBLICATION-DETERMINATES-QUESTION BANK
  1. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  2. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

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  3. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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  4. Factorize the following. [[a,b,c],[b+c,c+a,a+b],[a^2,b^2,c^2]]

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  5. Factorize the following. [[x,2,3],[1,x+1,3],[1,4,x]]

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  6. Show that by eliminating alpha and beta from the equations. aialpha+...

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  7. Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]]=0

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  8. Prove the following : [[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]]-(5x+4)(4-x...

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  9. Prove the following : [[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,c...

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  10. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  11. Prove that the points : (x1,y1),(x2,y2),(x3,y3) are collinear if [[x...

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  12. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  13. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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  14. Given the equations x=cy+bz, y=az+cx and z=bx+ay where x,y and z a...

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  15. If ax+hy+g=0, hx+by+f=0 and gx+fy+c=lamda, find the value of lamda in ...

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  16. Write the number of solution of the following system of equation. x-2y...

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  17. Write the number of solution of the following system of equation. x-y=...

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  18. Write the number of solution of the following system of equation. 2x+y...

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  19. Write the number of solution of the following system of equation. 3x+2...

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  20. Write the number of solution of the following system of equation. 2x+3...

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