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Q21Q

Expert-verifiedFound in: Page 93

Book edition
5th

Author(s)
David C. Lay, Steven R. Lay and Judi J. McDonald

Pages
483 pages

ISBN
978-03219822384

**Suppose the last column of AB is entirely zero but B itself has no column of zeros. What can you say about the columns of A?**

The columns of *A *are linearly dependent.

Consider \({b_p}\) to be the last column of *B.* The last column of \(AB\) should be zero, according to the hypothesis.

Here, \(A{b_p} = 0\). On the other hand, *B *contains no column of zeros; therefore, \({b_p}\) is not the zero vector. The equation \(A{b_p} = 0\) represents the linear dependence relation among the columns of *A*.

Thus, the columns of *A *are linearly dependent.

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