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Prove that {:|( a^(2) , bc, ac+c^(2)),( ...

Prove that `{:|( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) |:} =4a^(2) b^(2) c^(2) `

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Using the property of determinants and without expanding {:|( -a^(2) , ab,ac),( ba,-b^(2) , bc) ,( ca, cb, -c^(2)) |:} =4a^(2) b^(2) c^(2)

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)) |:}

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

|{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2):}|=4a^2b^2c^2

The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)+10)| is

|{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|= ?

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

Prove that, abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)) =1+ a^2+b^2+c^2 .

If a^(2) + b^(2) + c^(2) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

Prove that [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c^2 .

NCERT BANGLISH-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. Evaluate {:|( x,y , x+y),( y,x+y,x),( x+y,x,y)|:}

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  9. Evaluate {:|(1,x,y),( 1,x+y,y),( 1,x,x+y)|:}

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  10. Using properties of determinants in Exercises prove that : {:|( alph...

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

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  12. {:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) (...

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  13. {:|( 1,1+p,1+p+q),( 2,3+2p,4+3p+2q),( 3,6+3p,10+6p+3q)|:}=1

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  14. {:|( sin alpha , cos alpha ,cos (alpha +delta) ),( sinbeta, cos beta,c...

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  15. Solve the system of equations (2)/( x) + ( 3)/( y) +(10 )/( z) = 4 ...

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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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