Help: properties of Determinants/cramer's rule section

Linear spaces and subspaces, linear transformations, bases, etc.
Jbsmith11
Posts: 2
Joined: Mon Mar 28, 2011 3:54 pm
Contact:

Help: properties of Determinants/cramer's rule section

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.

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

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

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.

$r^n$ now you figure out why.

Use: if $A,B$ are square matrices then $\det(AB)=\det(A)\det(B)$

use: $A^{-1}=\frac{1}{\det(A)}adj(A)$

Jbsmith11
Posts: 2
Joined: Mon Mar 28, 2011 3:54 pm
Contact:

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

Perfect, your hints really helped. I appreciate it.