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# Study Guide for MATH 290 at KU

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This 3 page Study Guide was uploaded by an elite notetaker on Friday February 6, 2015. The Study Guide belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 33 views.

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Date Created: 02/06/15

Preparation for Final Exam Math 290 December 2008 Kamran Reihani 1 Consider the following system of linear equations z13234 0 z14234 1 31722374 0 a Determine whether the system is consistent b If the system is consistent write the solution in the form x X17 xh where xp is a particular solution and xh is a solution of the corresponding homogeneous equation 2 Find the inverse of the matrix using Gauss Jordan elimination 3 Find all values of A for which the following matrix is non singular 72 A 3 1 2 A 1 11 18 4 Use the adjoint of 1 75 71 1 0 2 to nd A l7 if possible 5 Find a basis and the dimension of the following subspaces of R4 a 35 7 2124125 7 3t7u Stu E R b 75 7 21125 7 2t10u74t7 121135 t3u Stu E R 6 Find the dimension of the subspace of R4 spanned by S 2573 i272732 7513722 1 7535 by nding a basis for it 7 Express the vector V 421 as a linear combination of the vectors V1 012V2 7102 and V3 321 8 Find the least square regression line for the points 72 4 713 03 1 2 and 2 2 9 Find the volume ofthe tetrahedron whose vertices are 123 03 71 140 and 052 1 0 1 10 ls the matrix 0 2 71 digonalizable 0 0 75 11 Find a basis of R3 containing the vectors 123 and 012 4 0 6 12 Let A 73 71 76 73 0 75 a Find the characteristic equation of A b C d Use the vectors from c to form an invertible matrix P such that P lAP is a diagonal matrix e Use d to compute A3 Compute the eigenvalues of A Find the corresponding eigenvectors of A 7 1 1 1 3 4 i i 1 2 1 5 7 13 Consider the matrix A i 71 0 1 71 73 l 2 71 4 0 73 a Find the rank of A and a basis for the row space of A b Find the nullity of A and a basis for the nullspace of A c Find a subset of the column vectors of A that forms a basis for the column space 14 Consider the matrix A OOOHH DOMH HOHHO OHOMM Find the rank of A Find the nullity of A a b c d e Find a basis for the column space of A Find a basis for the nullspace of A Find a basis for the row space of A

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