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|{:(0," "sinalpha,-cosbeta),(cosalpha," ...

`|{:(0," "sinalpha,-cosbeta),(cosalpha," "0," "sinbeta),(cos alpha,-sinbeta," "0):}|`

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"Evaluate "Delta ={:|( 0 , sin alpha ,-cos alpha ) ,( -sin alpha , 0 , sin beta ),( cos alpha , -sin beta , 0)|:}

|{:(cosalpha cos beta,cos alpha sin beta ,-sin alpha),(-sin beta,cos beta," "0),(sin alpha cosbeta ,sinalpha sin beta ,""cos alpha):}|

(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2 =

Evaluate {:|( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) |:} =0

Simplify (sinalpha+sinbeta)/(cosalpha-cosbeta)+(cosalpha+cosbeta)/(sinalpha-sinbeta)

Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,cosbeta,0),(sinalphacosbeta,sinalpha sinbeta,cosalpha)|

prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,sinalpha,0):}|^2=|{:(" "1,x,-x),(" "x,1," "x),(-x,x," "1):}| where x= sinalpha cosalpha

Prove that (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2) .

{:|( sin alpha , cos alpha ,cos (alpha +delta) ),( sinbeta, cos beta,cos (beta+delta )),(sin gamma , cos gamma , cos ( gamma +delta ))|:}=0

Prove that (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)dot

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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