MA 405 Test 3 Study Guide

MA 405 Test 3 Study Guide - MA 405 Test 3 - Study Guide...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MA 405 April 12, 2009 Test 3 - Study Guide The topics for Test 3 are covered in Sections 6.1 - 6.3, 5.1 - 5.5 in the textbook. Learning objectives: define and compute eigenvalues, eigenvectors, eigenspaces; recognize diagonalizable matrices; be able to write a diagonalizable matrix as A = PDP - 1 , for some invertible matrix P and diagonal matrix D ; use it to compute powers of A . apply the dot product, and use its properties; relationship between the dot product and matrix mul- tiplication; identify orthogonal subspaces; define the orthogonal complement of a vector space; define the four fundamental subspaces associated with a matrix; identify the relationship between them; compute the basis for each; use their properties; calculate the least-squares solution of an inconsistent linear system; compute the residual and the projection of a vector onto a subspace on R n ; calculate the equation of a line/parabola that best fits a given set of data; inner product spaces; definitions and properties; be able to check that an operation is an inner product; identify orthogonal/orthonormal sets of vectors in an inner product space; calculate the coordinates of a vector with respect to an orthogonal/orthonormal basis; identify orthogonal matrices and use their properties; 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Practice Questions 1. Consider the matrix A = 2 3 0 4 3 0 0 0 6 . (a) Find the eigenvalues of A . (b) Find bases for the eigenspaces corresponding to each eigenvalue of A . (c) Check that A is diagonalizable. Find the invertible matrix P that diagonalizes A and the diagonal matrix D which is similar to A, that is, P - 1 AP = D . (d) Use part (d) to calculate
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

MA 405 Test 3 Study Guide - MA 405 Test 3 - Study Guide...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online