Help: properties of Determinants/cramer's rule section  TOPIC_SOLVED

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Help: properties of Determinants/cramer's rule section

Postby Jbsmith11 on Mon Mar 28, 2011 4:02 pm

I need help with the following problems:

32. Find a formula for det (rA) when A is an n x n matrix and r is a scalar.

34. Let A and P be square matrices, with P invertible. Show that det [PA(P^-1)] = det A.

45. Suppose that all the entries in A are integers and det A = 1. Explain why all the entries in A^-1 are integers.
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Re: Help: properties of Determinants/cramer's rule section  TOPIC_SOLVED

Postby Martingale on Mon Mar 28, 2011 6:39 pm

Jbsmith11 wrote:I need help with the following problems:

32. Find a formula for det (rA) when A is an n x n matrix and r is a scalar.

34. Let A and P be square matrices, with P invertible. Show that det [PA(P^-1)] = det A.

45. Suppose that all the entries in A are integers and det A = 1. Explain why all the entries in A^-1 are integers.



now you figure out why.


Use: if are square matrices then

use:
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Re: Help: properties of Determinants/cramer's rule section

Postby Jbsmith11 on Tue Mar 29, 2011 2:46 am

Perfect, your hints really helped. I appreciate it.
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