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Show that {:|( 1+a,1,1),( 1,1+b,1) ,( 1...

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 `

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Show that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+(1)/(a)+(1)/(b)+(1)/(c)),(abcne0) .

|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

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

|{:(-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)

Answer the foll. Question : 2.show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]| = abc(1+1/a+1/b+1/c) , (abc != 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)

Show that |[-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 a, b, c are in A.P. then show that, a((1)/(b)+(1)/(c )), b((1)/(c )+(1)/(a)) and c((1)/(a)+(1)/(b)) are also in A.P.

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

The value of the determinant |((1)/(a),1,bc),((1)/(b),1,ca),((1)/(c),1,ab)| is -

NCERT BANGLISH-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Show that {:|( 1+a,1,1),( 1,1+b,1) ,( 1,1,1+c) |:}= abc ( 1+(1)/(a) +...

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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^(2)),( z,z^(2) , 1+pz^(2)...

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  13. {:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) (...

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

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

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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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