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

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)`

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RHS determinent is `=(a-b)^(2)(b-c)^(2)(c-a)^(2)`
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PREMIERS PUBLISHERS-MATRICES AND DETERMINANTS-PROBLEMS FOR PRACTICE .(II CHOOSE THE CORRECT OPTION FROM THE FOLLOWING)
  1. Sove that |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|^(2)=|(1+a^(2)+a^(4),1+...

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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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