Explore BrainMass

Explore BrainMass

    Taylor Series, Matrix Algebra and Complex Numbers

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A. Basic Mathematics - Please view the attachment for proper formatting of this question.

    1. Given that the Taylor series for the function

    1/(1-x) = 1 + x + x^2 + x^3 + ...,

    use this to show the following

    x/(1+x^2)^2 = x - 2x^3 + 3x^5 - ...

    log(1-x) = -x - x^2/2 - x^3/3 - x^4/4 - ...

    2. Consider complex number division (a + ib)/(c + id) which we express as re^ia. Using Euler's identity only, work out the precise form for the quotient's modulus r and argument alpha. Your calculations should not involve division of complex numbers.

    3. Using row operations evaluate the following determinant

    y-z z-x x-y
    z-x x-y y-z
    x-y y-z z-x

    4. Find the eigenvalues and eigenvectors of the following matrix

    3 3 3
    3 -1 1
    3 1 -1

    Verify that the eigenvectors are mutually orthogonal and hence diagonalise the matrix. Show all working.

    © BrainMass Inc. brainmass.com March 4, 2021, 8:45 pm ad1c9bdddf


    Solution Summary

    This solution looks at taylor series, matrix algebra and complex numbers in an attached Word document.