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Evaluate {:[( 102,18,36),( 1,3,4),( 17,...

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

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KUMAR PRAKASHAN-DETERMINANTS -Textbook Illustrations for Practice work
  1. Verify Property 2 for Delta=|{:(2,-3,5),(6,0,4),(1,5,-7):}|

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

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

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

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

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

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

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

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  9. 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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  10. 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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  11. Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1...

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

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

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

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

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

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

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

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

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

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