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question suppose x is an eigenvector of a corresponding to an eigenvalue lambdaa show that x is an eigenvector of 5i -
question construct a stage-matrix model for an animal species that has two life stages juvenile up to 1 year old and
question a herd of american buffalo bison can be modeled by a stage matrix similar to that for the spotted owls the
question solve the initial value problem x t ax t for t ge 0 with x 0 3 2 classify the nature of the origin as an
question make a change of variable that decouples the equation x ax write the equation x t py t and show the
question construct the general solution of x ax involving complex eigenfunctions and then obtain the general real
question will focus on matrices a with the property that at a show that every eigenvalue of such a matrix is
question let a be a complex or real n x n matrix and let x in cn be an eigenvector corresponding to an eigenvalue
question let a have the properties described in exercisea is the origin an attractor a repeller or a saddle point of
question verify the statements in the matrices are squareif b p-1ap and x is an eigenvector of a corresponding to an
question a is a 4 x 4 matrix with three eigenvalues one eigenspace is one-dimensional and one of the other eigenspaces
question construct a random integer-valued 4 x 4 matrix a and verify that a and at have the same characteristic
question let a be an n x n matrix and suppose a has n real eigenvalues lambda1 lambdan repeated according to
question it can be shown that the algebraic multiplicity of an eigenvalue lambda is always greater than or equal to the
question for the matrices list the real eigenvalues repeated according to their
question repeat exercise assuming u and v are eigenvectors of a that correspond to eigenvalues 1 and 3
question find the characteristic polynomial and the real eigenvalues of the
question if the null space of a 4 x 6 matrix a is 3-dimensional what is the dimension of the column space of a is col a
question the first four hermite polynomials are 1 2t - 2 4t2 and - 12t 8t3 these polynomials arise naturally in the
question let b be the basis of p3 consisting of the hermite polynomials in exercise 21 and let pt - 1 8t2 8t3 find
question concern the crystal lattice for titanium which has the hexagonal structure shown on the left in the
question for each subspacea find a basis for the subspace andb state the
question in use coordinate vectors to test the linear independence of the sets of polynomials explain your work1 - t2 t