[SPLIT] how to find the inverse of a 3-by-3 matrix

[mathfun]

I have another matrix question: How would I find the inverse of the following?

 [ 2  0  3 ]
 [ 1  5  2 ]
 [ 1 -3  1 ]

Thank you!

 

[stapel]

The usual process is to append the identity matrix, and then do row operations to move I from the one side to the other. In your case:

[ 2  0  3 | 1  0  0 ]
[ 1  5  2 | 0  1  0 ]
[ 1 -3  1 | 0  0  1 ]

The above matrix has the identity on the right-hand "half". Do row operations to convert the left-hand "half" into the identity, and then whatever you end up with on the right-hand will be the inverse of the original matrix.

Eliz.

 

[mathfun]

how do u noe thats its identity matrix?
because sometimes the 1 can be another number.

 

[stapel]

[H]ow do [you know] that['s] its identity matrix? ecause sometimes the 1 can be another number.

I'm sorry, but I don't understand your question. You started with a 3-by-3 matrix, so the identity one would use would have to be the 3-by-3 identity matrix.

And I'm afraid I don't know what you mean by the number 1 sometimes being some other number...?

Eliz.

 

[mathfun]

ok, let me reword my question.
do you always use
1 0 0
0 1 0
0 0 1]
for 3x3 matrices?

 

[stapel]

do you always use
1 0 0
0 1 0
0 0 1]
for 3x3 matrices?

Yes. To find the inverse of any n-by-n matrix, you do the set-up I showed previously, using the n-by-n identity.

Eliz.

 

[mathfun]

Sorry, I don't understand what row operations are. Do you mind doing this question for me or explaining it?
thanks.

 

[stapel]

I don't understand what row operations are. Do you mind doing this question for me or explaining it?

If they haven't covered row operations yet, then they must be expecting you to find the inverse in some other way. (There are other methods, but the one I outlined is customarily covered first.)

So which method are you supposed to be using? Determinants, maybe?

Thank you.

Eliz.

 

[mathfun]

I found the determinant.
how do i find the matrix of minors or something?

 

[stapel]

Minors and cofactors are icky, and awfully hard to type-set. Try online lessons for a general explanation.

Then see if you can do inverses and determinants in your graphing calculator, instead.... :shock:

Eliz.

 

[mathfun]

ok. thanks.