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Prove that the following. [[a+d,a+d+k,a+...

Prove that the following. `[[a+d,a+d+k,a+d+c],[c,c+b,c],[d,d+k,d+c]]`=abc

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`[[a+d,a+d+k,a+d+c],[c,c+b,c],[d,d+k,d+c]]`
`[[a,a,a],[c,c+b,c],[d,d+k,d+c]] (R_1~~R_1-R_3)`
`a[[1,1,1],[c,c+b,c],[d,d+k,d+c]]`
`a[[1,0,0],[c,b,-b],[d,k,c-k]]`
`(C_2=C_2-C_1,C_3=C_3-C_2)`
`a[[b,-b],[k,c-k]]`
=a(-bk+bc+bk)=abc
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MBD PUBLICATION-DETERMINATES-QUESTION BANK
  1. Prove that the following. [[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=...

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  2. Prove that the following. [[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3...

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  3. Prove that the following. [[a+d,a+d+k,a+d+c],[c,c+b,c],[d,d+k,d+c]]=ab...

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  4. Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+...

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

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

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  7. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

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

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  9. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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

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

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

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

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

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

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

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

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

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

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