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November 08, 2025, 04:46:25 am
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Author Topic: Inverting a 3x3 Matrix  (Read 2575 times)  Share 

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Odette

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Inverting a 3x3 Matrix
« on: March 11, 2008, 07:27:56 pm »
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Hello everyone, I'm having a bit of trouble with inverting a 3x3 matrix, I know how to invert a 2x2 matrix but i'm finding it hard to invert a 3x3 matrix...
Here's one I'm stuck on at the moment:
[ 4 2 1]
[-1 1 3]
[ 2 1 2]

Thanks to anyone who explains how to do this :)
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Ahmad

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Re: Inverting a 3x3 Matrix
« Reply #1 on: March 11, 2008, 07:32:47 pm »
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Augment that matrix with the 3x3 identity. Then perform row operations to transform the LHS part (the matrix above) to become the 3x3 identity, then the RHS part will be the inverse.
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ed_saifa

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Re: Inverting a 3x3 Matrix
« Reply #2 on: March 11, 2008, 07:41:25 pm »
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Have you learnt about the adj of a matrix and stuff? Or you could just use a calculator
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Odette

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Re: Inverting a 3x3 Matrix
« Reply #3 on: March 11, 2008, 07:47:29 pm »
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Oh we haven't learnt about the adj of a matrix... i have to invert it without using a calculator...

Ahmad do you mean...
[ 4 2 1|100]
[-1 1 3|010]
[ 2 1 2|001]
?
and then perform row operations so that the LHS becomes the identity matrix?
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ed_saifa

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Re: Inverting a 3x3 Matrix
« Reply #4 on: March 11, 2008, 07:48:46 pm »
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is this for mme cas or what?
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"It's not a community effort"
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Ahmad

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Re: Inverting a 3x3 Matrix
« Reply #5 on: March 11, 2008, 07:50:11 pm »
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Quote from: Odette on March 11, 2008, 07:47:29 pm
Oh we haven't learnt about the adj of a matrix... i have to invert it without using a calculator...

Ahmad do you mean...
[ 4 2 1|100]
[-1 1 3|010]
[ 2 1 2|001]
?
and then perform row operations so that the LHS becomes the identity matrix?

Yup. Then the RHS will be the inverse.
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Odette

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Re: Inverting a 3x3 Matrix
« Reply #6 on: March 11, 2008, 07:52:09 pm »
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Oh ok thanks ! I thought that's what I had to do but I wasn't sure >.<
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Odette

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Re: Inverting a 3x3 Matrix
« Reply #7 on: March 11, 2008, 09:00:35 pm »
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Seriously thank you =) I finally figured out the answer hehe
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sheepz

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Re: Inverting a 3x3 Matrix
« Reply #8 on: March 11, 2008, 09:10:57 pm »
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i thought my teacher said they wouldnt give us matrices more than 2x2 in the non-calculator section...
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Odette

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Re: Inverting a 3x3 Matrix
« Reply #9 on: March 11, 2008, 09:28:50 pm »
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Quote from: sheepz on March 11, 2008, 09:10:57 pm
i thought my teacher said they wouldnt give us matrices more than 2x2 in the non-calculator section...

Are you talking about vce maths?
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