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Find minors and cofactors of the element...

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`

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`a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0`
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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

KUMAR PRAKASHAN-DETERMINANTS -Textbook Illustrations for Practice work
  1. If x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z...

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

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  3. Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1...

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  4. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  5. Find the minor of elements 6 in the determinant Delta=|{:(1,2,3),(4,...

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  6. Find minors and cofactors of all the elements of the determinant |{:(1...

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  7. Find minors and cofactors of the elements a(11),a(21) in the determina...

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  8. Find minors and cofactors of the elements of the determinant |{:(2,-3,...

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  9. Find adj A for A = {:[( 2,3),( 1,4) ]:}

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  10. If A=[{:(1,3,3),(1,4,3),(1,3,4):}] , then verify that A adjA=|A|I. Als...

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  11. If A=[{:(2,3),(1,-4):}] and B=[{:(1,-2),(-1,3):}] then verify that (AB...

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  12. Show that the matrix A=[{:(2,3),(1,2):}] satisfies the equation A^2-4A...

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  13. Solve the system of equations {:(2x+5y=1),(3x+2y=7):},

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  14. Solve system of linear equations , using matrix method if exists 4x-...

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  15. The sum of three numbrs is 6. If we multiply third number by 3 and add...

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  16. If a,b,c are positive and unequal, show that value of the determinant ...

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  17. If a,b,c are in A.P find value of |{:(2y+4,5y+7,8y+a),(3y+5,6y+8,9y+...

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  18. show that [((x+y)^2 , zx , zy),( zx, (z+y)^2 ,xy),(zy,xy,(z+x)^2)]=2...

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  19. Solve following system using matrix x-y+2z =1 , 2y -3z =1, 3x...

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  20. Prove that |{:(a+bx,c+dx,p+qx),(ax+b,cx+d,px+q),(mu,vartheta,omega):}|...

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