Math Is Fun Forum

Gate2015

Member

Registered: 2015-01-03

Posts: 13

Matrix problems

plz solve left two question:

7. Show that if abab = aabb, then it must be that ab = ba.
8. Show that the matrix [1 2][2 1] * [3 2][1 2] does not equal [3 2][1 2] * [1 2][2 1] (It may be noted that matrices of integers are groups). This would mean that matrices are not abelian.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Matrix problems

Hi;

For 8 why do you not multiply and find out?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Matrix problems

hi Gate2015

Welcome to the forum. 

Q7.  Multiply both sides on the right by inverse b and then on the left by inverse a.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Matrix problems

hi Gate2015

Welcome to the forum. 

Q7.  Multiply both sides on the right by inverse b and then on the left by inverse a.

Bob

Except the inverses might not exist.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Matrix problems

hi Stefy,

Yes, I agree.  But how else to do this?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Matrix problems

hi Stefy,

Yes, I agree.  But how else to do this?

Bob

There is no way to do it, because it isn't true.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Matrix problems

What exactly are you saying is not true ?

If both inverses exist, then it is easy to prove.  So I'm guessing that you are saying that if one or more inverses don't exist then you can prove that ab ≠ ba.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Matrix problems

I'm saying that if both matrices aren't invertible, then there are cases where ab≠ba. I am not saying it's always the case if at least matrix is singular, because it isn't case (any matrix, singular or not, commutes with the identity matrix).

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Matrix problems

OK, but you ought to provide a counter example. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Matrix problems

Of course. We should consider:

Last edited by anonimnystefy (2015-01-04 07:13:31)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Matrix problems

But is abab = aabb ?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Matrix problems

Yep, it is.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.