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

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

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The correct Answer is:
a+b+c+1
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|{:(-1,b,c),(a,-1,c),(a,b,-1):}|=(a+1)(b+1)(c+1)((a)/(a+1)+(b)/(b+1)+(c)/(c+1)-1)

If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c +a,a +b,b +c)| = k |(a,b,c),(c,a,b),(b,c,a)| , then the value of k, is 1 b. 2 c. 3 d. 4

If D= |{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}| and A_1,B_1,C_1 etc. are the respective cofactors of the elements a_1,b_1,c_1 etc. then D will be-

|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

By using properties of determinants , show that : (i) {:|( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))|:}=(a-b)(b-c) (c-a) (ii) {:|( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))|:} =( a-b) (b-c)( c-a) (a+b+c)

|{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0

|{:(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=(b-c)(c-a)(a-b)(bc+ca+ab)

|{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|

If |{:(a,b,1),(b,c,1),(c,a,1):}|=2010 and if |{:(c-a,c-b,ab),(a-b,a-c,bc),(b-c,b-a,ca):}|-|{:(c-a,c-b,c^(2)),(a-b,a-c,a^(2)),(b-c,b-a,b^(2)):}|=p , then the number of positive divisors of p is

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

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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