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question find an orthonormal basis of the subspace spanned by the vectors in exerciseexercise the given set is a basis
question in parts a-d let u be the matrix formed by normalizing each column of the matrix a in exercisea compute utu
question determine which sets of vectors are orthonormal if a set is only orthogonal normalize the vectors to produce
question the matlab command roots p computes the roots of the polynomial equation p t 0 read a matlab manual and then
question use a matrix program to diagonalizeif possible use the eigenvalue command to create the diagonal matrix d if
question find a the largest eigenvalue andb the eigenvalue closest to zero in each case set x0 1 0 0 0 and carry out
question use the inverse power method to estimate the middle eigenvalue of the a in example with accuracy to four
question suppose is an eigenvalue of the b in exercise and that x is a corresponding eigenvector so that a - alphai-1x
question apply to a 3 x 3 matrix a whose eigenvalues are estimated to be 4 -4 and 3if the eigenvalues close to 4 and -4
q1 two spherical conductors b and c having equal radii and carrying equal charges in them repel each other with a force
question a common misconception is that if a has a strictly dominant eigenvalue then for any sufficiently large value
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