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QuantumJG's first year uni maths revision thread.

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QuantumJG:
Show that if A is an m x n matrix and A(BA) is defined, then B is an n x m matrix.

Firstly let the size of B = y x z

if A(BA) is defined, then BA is defined => z = m

therefore the size of matrix BA is y x n, so for A(BA) to be defined => y = n

=> size of B is n x m. 

Is that an adequate proof? 

jimmy999:
If you wanted to extend it you could say the number of columns of the first one must equal the number of rows of the second one. Something like that. I'm not exactly sure how detailed proofs need to be

QuantumJG:
Let matrix , be a matrix that represents all 2 x 2 matrices

Then AB = BA when B is either

or

Show that matrix A which satisfies the above must be a scalar matrix.

QuantumJG:
A scalar matrix is a matrix where all diagonal entries are equal, but I'm confused as to how to show A is a scalar matrix.

Voltaire:
why are you reviewing the intro to matrixies stuff..?

you should do like change of basis, orthonormal set's, then diagonalization and conics.
you gotta understand how it all links up etc, dont be doing these isolated defition type Q's

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