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|[1,a,bc] , [1,b,ca] , [1,c,ab]|=...

`|[1,a,bc] , [1,b,ca] , [1,c,ab]|=`

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`= ( a-b)(b-c) (c-a) `
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Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1):}|=1+a^2+b^2+c^2

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NCERT GUJARATI-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. |[1,a,bc] , [1,b,ca] , [1,c,ab]|=

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  2. Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...

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  3. Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...

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  4. Evaluate |cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinal...

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  5. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

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  6. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

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  7. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

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  8. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  9. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

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  10. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

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  11. Using peoperties of determinants in questions 11 to 15, prove that : ...

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  12. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

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  13. Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...

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  14. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

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  15. Without expanding, show that the value of each of the determinants is ...

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  16. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

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  17. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

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  18. Choose the correct answer in questions 17 to 19: If x, y, z are non...

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  19. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

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