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Without expanding prove that Delta=|{:...

Without expanding prove that
`Delta=|{:(x+y,y+z,z+x),(z,x,y),(1,1,1):}|=0`

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If x,y,z are all different from zero and |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=0 then value of x^(-1)+y^(-1)+z^(-1) is ".........."

KUMAR PRAKASHAN-DETERMINANTS -Textbook Illustrations for Practice work
  1. Using the property of determinants and without expanding prove the fol...

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

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

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

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

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  6. 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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  7. 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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  8. Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1...

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

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

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

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

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

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

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

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

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

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

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

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

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