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Find the mirrors and cofactors of the e...

Find the mirrors and cofactors of the elements of the determinant
`Delta = |{:(a_(11), a_(12), a_(13)), (a_(21), a_(22), a_(23)), (a_(31), a_(32), a_(33)):}|`

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Find minors and cofactors of the elements a_(11),a_(21) in the determinant Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}|

Find minors and cofactors of the elements of the determinant |{:(2,-3,5),(6,0,4),(1,5,-7):}| and verify that a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij) is a determinant obtained by deleting ith row and jth column then then |{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}|=Delta^(2). If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =5 and Delta =|{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| then sum of digits of Delta^(2) is

Statement -1 Consider the determinant Delta=|{:(a_(1)+b_(1)x^(2),a_(1)x^(2)+b_(1),c_(1)),(a_(2)+b_(2)x^(2),a_(2)x^(2)+b_(2),c_(2)),(a_(3)+b_(3)x^(2),a_(3)x^(2)+b_(3),c_(3)):}|=0, where a_(i),b_(i),c_(i) in R (i=1,2,3) and x in R Stement -2 If |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| =0, then Delta =0

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and A_(ij) Cofators of a_(ij) then value of Delta is given by ……..

If a_(1),b_(1),c_(1),a_(2),b_(2),c_(2) "and" a_(3),b_(3),c_(3) are three digit even natural numbers and Delta=|{:(c_(1),a_(1),b_(1)),(c_(2),a_(2),b_(2)),(c_(3),a_(3),b_(3)):}| , then Delta is

Find the relation between acceleration of blocks a_(1), a_(2) and a_(3) .

Write the first five terms of the sequences in obtain the corresponding series: a_(1)= a_(2)= 1, a_(n)= a_(n-1) + a_(n-2), n gt 2

Find the indicated terms in each of the sequences whose n^("th") terms are: a_(n) =4n-3,a_(17) ,a_(24)

Find the indicated terms in each of the sequences whose n^(th) term is given: a_(n)= (-1)^(n) (n^(2)-1), a_(13)

NCERT GUJARATI-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Find the mirrors and cofactors of the elements of the determinant D...

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  2. Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...

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  3. Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...

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  4. Evaluate |cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinal...

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  5. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

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  6. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

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  7. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

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  8. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  9. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

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  10. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

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  11. Using peoperties of determinants in questions 11 to 15, prove that : ...

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

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  13. Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...

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  14. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

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  15. Without expanding, show that the value of each of the determinants is ...

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  16. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

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  17. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

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  18. Choose the correct answer in questions 17 to 19: If x, y, z are non...

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  19. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

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