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If a,b and c are real numbers, and De...

If a,b and c are real numbers, and
`Delta ={:[( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) ]:}=0`
Show that either `a+b+c=0 "or" a= b= c . `

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NCERT TAMIL-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin thet...

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

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

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

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

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

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

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  8. Let A = {:[( 1,2,1),(2,3,1),(1,1,5) ]:} Verify that (A^(-1) )^(-1) =...

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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. solve {:[( 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,4+3p+2q),( 3,6+3p,10+6p+3q)]:}=1

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  15. Without expanding evaluate the determinant |(sinalpha,cosalpha,sin(alp...

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  16. Solve system of linear equations , using matrix method 2x+ 3y + ...

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

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

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

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