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QuantumJG's first year uni maths revision thread.

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QuantumJG:

--- Quote from: Voltaire on January 04, 2010, 09:35:16 pm ---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

--- End quote ---

--- Quote from: Voltaire on January 04, 2010, 09:35:16 pm ---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

--- End quote ---

Lol. I have already done that.

I'm just going through some proof questions I didn't get during the semester.

QuantumJG:
This question is really annoying me!

Let A be a square matrix satisfying A2 = A and let matrix B be a square matrix the same size as A.

Show that (AB - ABA)2 = 0 (obviously the 0 matrix)

The only thing I can think of is trying to prove AB = ABA, which would be easy if ABA = AAB = A2B = AB.

zzdfa:
(AB-ABA)^2
=(AB-ABA)(AB-ABA)
=AB(AB-ABA)-(ABA)(AB-ABA)        matrix multiplication is distributive
=ABAB-ABABA-ABAAB+ABAABA         and again
=ABAB-ABABA-ABAB+ABABA          A^2=A
=0
sometimes you just have to get your hands dirty.

zzdfa:

--- Quote from: QuantumJG on January 04, 2010, 06:11:35 pm ---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.

--- End quote ---


Let be the first matrix and be the second.

then you have 2 equations:







Get those equations in terms of a,b,c,d (do the multiplication e.g. )

QuantumJG:

--- Quote from: zzdfa on January 05, 2010, 07:25:12 pm ---(AB-ABA)^2
=(AB-ABA)(AB-ABA)
=AB(AB-ABA)-(ABA)(AB-ABA)        matrix multiplication is distributive
=ABAB-ABABA-ABAAB+ABAABA         and again
=ABAB-ABABA-ABAB+ABABA          A^2=A
=0
sometimes you just have to get your hands dirty.

--- End quote ---

Thanks.

I suck at matrix proofs. :(

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