I given the question and answer for both of the problems can you please please do it step by step **Question 8.40:** The columns of a matrix $ A $ are linearly dependent. Find $ \text{det}(A) $.**Question 8.41:** Let $ A $ and $ B $ be $ 5 \times 5 $ matrices such that $ AB $ is invertible. Find $\text{Rank}(A)$ and $\text{Nullity}(B)$. **Section 8.40**0.**Section 8.41**5, 0.---This transcription provides sections and their respective notations. Note that the periods indicate the end of each section. Further context or material may be necessary for a full understanding of these sections.

If the columns of matrix A are linearly dependent, it means that at least one column can be…

Answered: 8.40. The columns of a matrix A are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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8.40. The columns of a matrix A are linearly dependent. Find det(A). 8.41. Let A and B be 5 x 5 matrices such that AB is invertible. Find Rank(A) and Nullity(B).