### This problem asks the student to find the eigenvalues of a 3x3 matrix.

Find the eigenvalues of the following matrix Q = Mat[0 0 -2; 1 2 1; 1 0 1]. (See attached file for clearer version.)

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Find the eigenvalues of the following matrix Q = Mat[0 0 -2; 1 2 1; 1 0 1]. (See attached file for clearer version.)

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Uxx means second derivative with respect to x Uyy means second derivative with respect to y Uxx + Uyy = 0, 0 < x < pi, 0 < y < 1 Ux(0,y) = 0 = U(pi,y), 0 < y < 1 U(x,0) = 1, U(x,1) = 0, 0 < x < pi Please show all work including how eigenvalues and eigenvectors are derived. Thank you

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S_5 = Aut(A_5)

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Are the following examples linear transformations from p3 to p4? If yes, compute the matrix of transformation in the standard basis of P3 {1,x,x^2} and P4 {1,x,x^2,x^3}. (a) L(p(x))=x^3*p''(x)+x^2p'(x)-x*p(x) (b) L(p(x))=x^2*p''(x)+p(x)p''(x) (c) L(p(x))=x^3*p(1)+x*p(0)

In the standard basis of P3 (i.e. {1,x,x^2}) p(x)=3-2x+5x^2, that is, it has coordinates p=(3,-2,5). Find the coordinates of this vector (polonomial) in the basis {1-x,1+x,x^2-1}

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Please see the attached file for the fully formatted problems. Solve the following system of equations: 4/x - 9/y = -1 -7/x + 6/y = -3/2

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