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Verify Property 2 for Delta=|{:(2,-3,5),...

Verify Property 2 for `Delta=|{:(2,-3,5),(6,0,4),(1,5,-7):}|`

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The correct Answer is:
`Delta_1=-Delta`
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Verify: The value of the determinant remains unchanged if its rows and columns are interchanged. Delta=|{:(2,-3,5),(6,0,4),(1,5,-7):}|

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

Using Cofactors of elements of second row, evaluate Delta=|{:(5,3,8),(2,0,1),(1,2,3):}|

Find the minor of elements 6 in the determinant Delta=|{:(1,2,3),(4,5,6),(7,8,9):}|

Find the minors and cofactors of elements '-3^(prime),\ \ ^(prime)5^(prime),\ \ -1^(prime)&\ '7' in the determinant |{:(2,-3, 1), (4, 0, 5),(-1, 6, 7):}|

Statement -1 The value of the determent |{:(1,2,3),(4,5,6),(7,8,0):}|ne 0 Statement -2 Neither of two rows rows or columns of |{:(1,2,3),(4,5,6),(7,8,0):}| is identical.

Verify the following : (-1, 2, 1), (1, -2, 5), (4, -7, 8) and (2, -3, 4) are the vertices of a parallelogram.

Verify the following : (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle.

Find the area of the triangle whose vertices are : (1) (2,3), (-1, 0), (2,-4) (2) (-5, -1),(3,-5), (5,2)

|{:(5^2,5^3,5^4),(5^1,5^2,5^3),(5^3,5^4,5^4):}|=.......

KUMAR PRAKASHAN-DETERMINANTS -Textbook Illustrations for Practice work
  1. Find values of x for which |{:(3,x),(x,1):}|=|{:()3,2),(4,1):}|

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  2. Verify: The value of the determinant remains unchanged if its rows and...

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  3. Verify Property 2 for Delta=|{:(2,-3,5),(6,0,4),(1,5,-7):}|

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  4. Evaluate Delta =|{:(3,2,3),(2,2,3),(3,2,3):}|

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  5. Evaluate {:[( 102,18,36),( 1,3,4),( 17,3,6)]:}

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  6. Using the property of determinants and without expanding prove the fol...

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  7. Prove that |{:(a,a+b,a=b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}...

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  8. Without expanding prove that Delta=|{:(x+y,y+z,z+x),(z,x,y),(1,1,1):...

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  9. Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

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  10. Prove that {:[( b+c,a,a), ( b,c+a,b),( c,c,b+a) ]:}

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  11. 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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  12. 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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  13. Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1...

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

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

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

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

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

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

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

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