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prove that : |{:(1,a,b),(-a,1,c),(-b,-c,...

prove that : `|{:(1,a,b),(-a,1,c),(-b,-c,1):}|=1+a^2+b^2+c^2`

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Without expanding the determinant, prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a) .

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Without expanding prove that |{:(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab):}|=0

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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2A
  1. |{:(1,a,bc),(1,b,ca),(1,c,ab):}|

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  2. |{:(1," "1," "1),(1,1+x," "1),(1," "1,1+y):}|

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  3. |{:(1+a," "b," "c),(" "a,1+b," "c),(" "a," "b,1+c):}|

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  4. |{:(" "1," "z,-y),(-z," "1," "x),(" "y,-x," "1):}|

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  5. |{:(-a," "a," "a),(" "b,-b," "b),(" "c," "c,-c):}|

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  6. |{:(0," "sinalpha,-cosbeta),(cosalpha," "0," "sinbeta),(cos alpha,-sin...

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  7. write minor and cofactor ; |{:(5,2),(0,-1):}|

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  8. write minor and cofactor ; |{:(-1,4),(2,3):}|

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  9. write down the minor and cofactor |{:(1,a,bc),(1,b,ca),(1,c,ab):}|

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  10. write down the minor and cofactor |{:(0,2,6),(1,5,0),(3,7,1):}|

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  11. Evaluate the determinant |{:(" "2,3,-5),(" "7,1,-2),(-3,4," "1):}| ...

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  12. If [.] denotes the greatest ingeter less then or equal to the real num...

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  13. Evalute the determinant D=|{:(" "1," "sintheta,1),(-sintheta," "1,si...

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  14. Find the minors and the cofactors of each element of the first column ...

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  15. If A=[{:(1,3),(2,1):}],find the determinant of the matrix A^2-2A.

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  16. If A =[{:(1,0,1),(0,1,2),(0,0,4):}], then show that |3A|=27|A|.

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  17. If A = [{:(2,5),(2,1):}] and B =[{:(4,-3),(2,5):}] ,verify that |AB|...

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  18. If f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasinthe...

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  19. Find the integral value of x if |{:(x^2,x,1),(0,2,1),(3,1,4):}|=28

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  20. prove that : |{:(1,a,b),(-a,1,c),(-b,-c,1):}|=1+a^2+b^2+c^2

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