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Questions of matrix polynomial Equation...

Questions of matrix polynomial Equation

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Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

Use Rollle's theorem to find the condition for the polynomial equation f(x)=0 to have a repeated real roots, Hence, or otherwise prove that the equation.

Which of the following polynomial equations could be used to represent the area of the trapezoid shown in the figure?

find the (monic ) polynomial equation of lowest degree whose roots are 1,3,5,7

Which of the graphs given below corresponds to linear polynomial or a quadratic polynomial ? Also, find the number of zeroes of the polynomial in each case.

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[[0,1],[-1,0]], find x\ a n d \ y such that (x I+y A)^2=A

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  2. If [(2,-1),(1,0),(-3,4)]A=[(-1,-8,-10),(1,-2,-5),(9,22,15)], find A.

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  3. Questions of matrix polynomial Equation

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  4. If Aa n dB are symmetric matrices of the same order, write whether AB-...

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  5. If A is a square matrix such that A^2=A ,t h e n(I+A)^3-7A is equal ...

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  6. If A is a square matrix such that A^2=A , then write the value of 7A-(...

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  7. Construct a 3xx4 matrix A=[a(i j)] whose elements are given by (i)a...

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  8. If [x-y2x+z2x-y3z+w]=[-1 5 0 13] , find x ,\ y ,\ z ,\ wdot

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  9. Find dy/dx if x+y =( tanx)^2

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  10. A matrix has 12 elements. What are the possible orders it can have?

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  11. Find dy/dx If y= (sinx)^cosx .

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  12. A matrix has 12 elements. What are the possible orders it can have?

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  13. Construct a 2xx2 matrix A=[a(i j)] whose elements are given by a(i ...

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  14. Construct a 2xx3 matrix A=[a(i j)] whose elements are given by a(i ...

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  15. Construct a 3xx2 matrix A=[a(i j)] whose elements are given by a(i j...

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  16. Find x ,\ y ,\ z and w such that [(x-y,2z+w),(2x-y,2x+w)]=[(5, 3 ),(...

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  17. Consider the following information regarding the number of men and ...

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  18. If [(a+b,2),( 5,a b)]=[(6, 2),( 5, 8)] , find the values of a and b ...

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  19. For what values of x and y are the following matrices equal? A=[...

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  20. If a matrix has 8 elements, what are the possible orders it can hav...

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