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Prove that |(1,a,a^(2)),(1,b,b^(2)),(1,c...

Prove that `|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=(a-b)(b-c)(c-a)`

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The correct Answer is:
`rArr (a-b)(b-c)(c-a)`
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By using properties of determinants , show that : (i) {:[( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))]:}=(a-b)(b-c) (c-a) (ii) {:[( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))]:} =( a-b) (b-c)( c-a) (a+b+c)

Prove that |(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)|= 0 .

Sove that |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|^(2)=|(1+a^(2)+a^(4),1+ab+a^(2)b^(2),1+ac+a^(2)c^(2)),(1+ab+a^(2)b^(2),1+b^(2)+b^(4),1+bc+b^(2)c^(2)),(1+ac+a^(2)c^(2),1+ba+b^(2)c^(2),1+c^(2)+c^(4))| and hence show RHS determinent is =(a-b)^(2)(b-c)^(2)(c-a)^(2)

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|

Prove that |(1/a^(2),bc,b+c),(1/b^(2),ca,c+a),(1/c^(2), ab, a+b)|=0

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

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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)) ]:}

Prove that Delta = |{:(1,,1,,1),(a,,b,,c),(bc+1^(2),,ac+b^(2),,ab+c^(2)):}| = 2(a-b)(b-c)(c-1)

PREMIERS PUBLISHERS-MATRICES AND DETERMINANTS-PROBLEMS FOR PRACTICE .(II CHOOSE THE CORRECT OPTION FROM THE FOLLOWING)
  1. Prove that |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=(a-b)(b-c)(c-a)

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  2. If a(ij)=i^(2)-j and A=(a(ij))(2xx2)is:

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  3. Solve|(x-1,2),(3,x-2)|=0

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  4. If 2x+[(3,1),(5,-3)]=[(-1,5),(3,-1)]then x is

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  5. If A=[(3,2,1),(0,4,2),(1,2,3)]and B=[(3,2,0),(4,8,0),(-1,6,2)],then

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  6. If the points (2,-4)(6,2)(4,x) are collinear than x is:

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  7. If the square matrix |(alpha,Beta),(Beta,-alpha)|is a unit matrix of o...

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  8. A=[(0,-2,1),(2,0,-4),(-1,0,0)]then A is

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  9. If A=[(2x,2y,2z),(2a,2b,2c),(2p,2q,2r)]and Delta =[(x,y,z),(a,b,c),(p,...

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  10. If A+2I=[(6,2),(3,-4)],then A(A+I)=

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  11. Find the matrix A if[(1,2),(0,1)]A=[(6,1),(2,1)]

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  12. Find the value of x for which A=[(e^(2x+1),e^(x-2)),(e^(2-x),e^(x-7))]...

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  13. If A is (a(ij))(mxxn),B=(b(ij)(nxxp)),C=(c(ij)(pxxq))Then (ABC)^(T) wi...

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  14. Ifr A is a skew symmetrix matrix of order 3 and B is column matrix of ...

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  15. If A=[(2,4,-5),(3,1,-2),(0,2,-3)],find the coefficient of order 3:

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  16. If A and B are square matrix of same order then (A-B)^(T) is:

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  17. |((x+1/x)^(2),(x-1/x)^(2),1),((y+1/y)^(2),(y-1/y)^(2),1),((z+1/z)^(2),...

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  18. Evaluate |(45,71,26),(35,-21,14),(77,50,40)|:

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  19. if|(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b)|=k(abc).Then k is:

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  20. The area ofDelta with vertices (-2,-3),(3,2),and (-1,x).Then x is:

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  21. Which of the followinf is not true about the matrix[(5,0,0),(0,0,0),(0...

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