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Evaluate Delta = {:[ (1,a,bc),( 1,b,ca)...

Evaluate ` Delta = {:[ (1,a,bc),( 1,b,ca),(1,c,ab)]:}`

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The correct Answer is:
`= ( a-b)(b-c) (c-a) `
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If Delta_(1)=|(1,a,bc),(1,b,ca),(1,c,ab)|,Delta_(2)=|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))| then

Show that {:[( 1+a,1,1),( 1,1+b,1) ,( 1,1,1+c) ]:}= abc ( 1+(1)/(a) +(1)/(b) +(1)/(c) ) = abc +bc +ca +ab

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)) ]:}

|(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=

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

Without expanding the determinant, prove that (i) |{:(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)):}| (ii) |{:(ax,by,cz),(x^(2),y^(2),z^(2)),(1,1,1):}|=|{:(a,b,c),(x,y,z),(yz,zx,xy):}| (iii) |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|

NCERT TELUGU-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Evaluate Delta = {:[ (1,a,bc),( 1,b,ca),(1,c,ab)]:}

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  2. Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin thet...

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

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  4. Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),...

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  5. If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a...

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  6. Solve the equation {:[( x+a,x,x),(x,x+a,x),(x,x,x+a) ]:}=0,ane 0

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  7. Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2...

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

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  9. Evaluate {:[( x,y , x+y),( y,x+y,x),( x+y,x,y)]:}

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  10. Evaluate {:[(1,x,y),( 1,x+y,y),( 1,x,x+y)]:}

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  11. Using properties of determinants in Exercises prove that : {:[( alph...

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  12. {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(3)),( z,z^(2) , 1+pz^(3)...

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  13. Prove {:[( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) ]:} = 3( a+...

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  14. {:[( 1,1+p,1+p+q),( 2,3+2p,1+3p+2q),( 3,6+3p,1+6p+3q)]:}=1

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  15. Prove that {:[( sin alpha , cos alpha ,cos (alpha +delta) ),( sinbeta,...

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  16. If a,b,c are in A.P. then the determinant {:[( x+2,x+3,x+2a),( x+3,...

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  17. If x,y,z are nonzero real number , then the inverse of matrix A= {:[( ...

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  18. Let A={:[( 1,sin theta , 1),( -sin theta , 1, sin theta ),( -1 ,-sin ...

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