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Show that (a+1) is a factor of abs([(a+1...

Show that `(a+1)` is a factor of `abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])`

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ARIHANT PUBLICATION-DETERMINANTS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 5(A))
  1. Evaluate the following : [[2,-3,4],[-4,2,-3],[11,-15,20]]

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  2. Show that x=1 is a solution of [[x+1,3,5],[2,x+2,5],[2,3,x+4]]=0

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  3. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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  4. Show that [[a1,b1,-c1],[-a2,b2,c2],[a3,b3,-c3]]= [[a1,b1,c1],[a2,b2,...

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

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  6. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(ab...

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

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  9. 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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  10. 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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  11. Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

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

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

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

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

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

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

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

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

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