0

I have the following problem which I do not know how to solve. I found the statement to be a bit confusing. Here's the problem:

If $B=((b_{ij})) \in M_{n\times n}$ where $b_{ij}=1 \, \forall i,j$ and $A=(a-b)i_n+bB$

Prove that $|A|=(a-b)^{n-1}[a+(n-1)b]$

I found the $i_n$ notation to be a bit cofusing, so I do not really understand how matrix A was declared. Can anybody help me?

Facu50196
  • 117
  • 1
    Perhaps $i_n$ is meant to denote the $n \times n$ identity matrix. Where did you encounter this problem? Did you try looking for definitions of notation from the source? – Ben Grossmann Apr 07 '19 at 21:30
  • If $i_n$ is supposed to be an identity matrix, then I'd say that this question is a duplicate of this post – Ben Grossmann Apr 07 '19 at 21:31
  • Oh, it could be that. I was a bit confused since it was a lowercase $i$. Maybe it was a typing error. The problem is from a handout that was given in my university. I'll try to solve it assuming that the $i$ is the identity matrix. – Facu50196 Apr 07 '19 at 21:34
  • @Omnomnomnom I solved it assuming that $i$ was the identity matrix and I was able to get to the answer. So it is a duplicate. What do I have to do? Do I delete the question? – Facu50196 Apr 07 '19 at 21:53
  • No, leave it up. We'll vote to close it, but it is useful to have these duplicate questions around – Ben Grossmann Apr 07 '19 at 22:02
  • Ok, I'll do that. Thanks for the help! – Facu50196 Apr 07 '19 at 22:03

0 Answers0