Concept explainers
What are the ranks r for these matrices with entries i times j and i plus j? Write
Answer to Problem 1PS
Rank(A)=1
Rank(B)=2
Explanation of Solution
Given information:
Not requiring
Calculation:
Similarly,
So, the singular value decomposition has a division by
Multiply by
Therefore,
Now consider the matrix
First two columns of
Therefore,
Those pivot columns don't give the u's and v's of the SVD. For that we need eigenvalues and eigenvectors of
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Chapter 7 Solutions
Introduction to Linear Algebra, Fifth Edition
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