Recent content by aanandpatel

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    Finding the basis for a vector space

    Makes sense now - got it! Thanks a lot - help was much appreciated :)
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    Finding the basis for a vector space

    sorry had no idea how to matrices on the forum C = ##\begin{pmatrix} 1 & 2 \\ 3 & 6 \end{pmatrix}## A(my general matrix) = ##\begin{pmatrix} a & b \\ c & d \end{pmatrix}## CA=0 so when I multiplied, I got a+2c=0 b+2d=0 3a+6c=0 3b+6d=0 But two of those equations are the same and...
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    Finding the basis for a vector space

    Homework Statement Find a basis for the following vector space: The set of 2x2 matrices A such that CA=0 where C is the matrix : 1 2 3 6 The Attempt at a Solution I multiplied C by a general 2x2...
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    Complex Solutions

    Yes when I say x=0 it means that the 'real part' of the solution is 0
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    Complex Solutions

    2y = 0 and x=0
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    Complex Solutions

    Two complex numbers are only equal if their real parts are equal and their imaginary parts are equal so you may have to equate real and imaginary parts to find the values of x and y.
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    Implicit differentiation

    Thanks guys - helped a lot! :)
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    Implicit differentiation

    Homework Statement Find the coordinates of the stationary points on the curve: x^3 + (3x^2)(y) -2y^3=16 Homework Equations Stationary points occur when the first derivative of y with respect to x is equal to zero The Attempt at a Solution I implicitly differentiated the...
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    Relationship between roots and coefficients

    a fourth degree polynomial has 4 roots therefore alpha and beta are double roots?
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    Relationship between roots and coefficients

    The question says that the curves touch at the points A and B so I assumed they were tangential to each other at those points. Not sure how I would prove it otherwise seeing as I only have an x value for the points.
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    Relationship between roots and coefficients

    Homework Statement Homework Equations Sum of roots taken one at a time is -b/a Sum of roots taken two at a time is c/a three at a time is -d/a four at a time is e/a The Attempt at a Solution I did part one by solving the two equations...
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    CERN team claims measurement of neutrino speed >c

    Apologies for the mistake - was quoting Michio Kaku.
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    CERN team claims measurement of neutrino speed >c

    In 1987, there was a supernova in the Large Magellanic Cloud. This is roughly 50,000 light years away from the Earth. Scientists detected light from the supernova and neutrinos from the supernova at the exact same time meaning they have the exact same velocity. This experiment used distances of...
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    What is a constant

    It is a number that simply does not change and has a set, defined value. Pi, i (squareroot of -1) and e (Euler's number) are all examples of constants.
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    Use De Moivre's Theorem to prove this:

    Thanks a bunch - that helped a lot. Converted it into: [(secθ)(cosθ+isinθ)]^n + [(secθ)(cosθ-isinθ)]^n and it was easy from there. Cheers!
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