Thread: Write the given matrix as a product of elementary matrices

Hello,

Can someone help me understand this problem?

Write the given matrix as a product of elementary matrices

[ -3 1 ]
[ 2 2 ]

I'm confused by the process, can someone shed some light on how to do it?

Thanks,

Originally Posted by l flipboi l

Hello,

Can someone help me understand this problem?

Write the given matrix as a product of elementary matrices

[ -3 1 ]
[ 2 2 ]

I'm confused by the process, can someone shed some light on how to do it?

Thanks,

Do you know what elementary matrices are? Can you list the three 2x2 elementary matrices that this question is referring to?

I'm not sure, but the answer is:

[1 0][1 1][-4 0][1 0]
[0 2][0 1][ 0 1][1 1]

Not sure how to get this...

Originally Posted by l flipboi l

I'm not sure, but the answer is:

[1 0][1 1][-4 0][1 0]
[0 2][0 1][ 0 1][1 1]

Not sure how to get this...

This is not the answer to the question I asked.

If you don't know know what elementary matrices are, i don't see how you can hope to answer the question.

So the first step is to look up elementary matrices in your class notes, textbook or use Google.

My apologies, I wasn't sure what you meant by "list the three 2x2 elementary matrices that this question is referring to?"

But yes, I am familiar with Elementary Matrix and the Elementary operations.... I'm able to get some of the answer, but I keep getting stuck.

What i'm able to do is transform

[ -3 1 ]
[ 2 2 ]

to

[1 0]
[0 1]

now what do I do from there?

Here's what I have...

operations:

[1 5]
[2 2]

[1 5]
[1 1]

[1 5]
[0 -4]

[1 5]
[0 1]

[1 0]
[0 1]

I've been working on a problem similar to do, is it safe to say that you don't have to have it in the reduced echelon form?

for instance I can leave it as:

[1 4]
[0 1]

Then perform the operations for the identity?