MATH 3A Study Guide - Final Guide: Orthogonalization, Identity Matrix, Diagonal Matrix
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MATH 3A Full Course Notes
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Math 3a: extra final review questions: solve the following system of equations using any method you like. = 3 x2 +2x3: compute the subspaces n (a),n (at), col(a), col(at) for the following matrix, and check that the fundamental subspace theorem holds. Make a couple of skectches which illustrate the four subspaces and their relationship to one another. A : suppose that a is non-singular. Prove that at a is non-singular: prove that a is diagonalizable if and only if at is, let a be the matrix. 1: apply the gram schmidt orthogonalization process to compute an orthonormal basis of. Hence or otherwise, compute the orthogonal projection of the vector v : a square matrix is said to be orthogonal if at a = i where i is the identity matrix. Prove that the determinant of an orthogonal matrix must be 1: the vector space p2 = span{1, x, x2} together with the function (cid:90) 1.
