Page 442 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

T1. (Basis for Row Space) Some technology utilities provide a command for finding a basis for the row space of a matrix. If
your utility has this capability, read the documentation and then use your utility to find a basis for the row space of the matrix
in Example 6.

T2. (Basis for Column Space) Some technology utilities provide a command for finding a basis for the column space of a
matrix. If your utility has this capability, read the documentation and then use your utility to find a basis for the column space
of the matrix in Example 6.

T3. (Nullspace) Some technology utilities provide a command for finding a basis for the nullspace of a matrix. If your utility has

this capability, read the documentation and then check your understanding of the procedure by finding a basis for the

nullspace of the matrix A in Example 4. Use this result to find the general solution of the homogeneous system .

Section 5.6

T1. (Rank and Nullity) Read your documentation on finding the rank of a matrix, and then use your utility to find the rank of
the matrix A in Example 1. Find the nullity of the matrix using Theorem 5.6.3 and the rank.

There is a result, called Sylvester's inequality, which states that if A and B are matrices with rank and ,
T2. respectively, then the rank of satisfies the inequality
, where denotes the

smaller of and or their common value if the two ranks are the same. Use your technology utility to confirm this result

for some matrices of your choice.

Copyright © 2005 John Wiley & Sons, Inc. All rights reserved.