Math Is Fun Forum

deepz

Member

Registered: 2007-03-20

Posts: 10

linear algebra

Hi im stuck on this question, can anyone help please?

Let A and D be square nxn matrices. Show that if D is diagonal with
diagonal entries a1,....,an, that is dii = ai where D = (dij), then

a)AD is the matrix whose j-th column is aj times the j-th column of A
b)DA is the matrix whose i-th row is ai times the i-th row of A

thanks

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: linear algebra

This is really just by definition of matrix multiplication.  Take two 3x3 matrices as described in the problem, multiply them, and see what happens.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: linear algebra

remember that in a diagonal matrix A, A(i,j) = 0 wherever i ≠ j, so if you have something like

∑ A(i,k) from k = 1 to n (where 1 <= i <= n) then the only non zero term is A(i,i)
what happens if you have
∑A(i,k)B(i,k) from k = 1 to n?

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A logarithm is just a misspelled algorithm.