# Two Further Maths Questions

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1) How do you do 8c quickly if it is 1 mark and consequently 8d?

2) Why is my answer to 9c nothing like the show that?

2) Why is my answer to 9c nothing like the show that?

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(Original post by

1) How do you do 8c quickly if it is 1 mark and consequently 8d?

2) Why is my answer to 9c nothing like the show that?

**wbanner2001**)1) How do you do 8c quickly if it is 1 mark and consequently 8d?

2) Why is my answer to 9c nothing like the show that?

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#3

**wbanner2001**)

1) How do you do 8c quickly if it is 1 mark and consequently 8d?

2) Why is my answer to 9c nothing like the show that?

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#4

I think this is correct?? Let me know.

It’s just playing around with the matrix identities.

So essentially M^-1 is equal to the transposed Matrix

Hence why only 1 Mark. I have absolutely no idea if that correct though...

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(Original post by

I think this is correct?? Let me know.

It’s just playing around with the matrix identities.

So essentially M^-1 is equal to the transposed Matrix

Hence why only 1 Mark. I have absolutely no idea if that correct though...

**Silurianwarrior1**)I think this is correct?? Let me know.

It’s just playing around with the matrix identities.

So essentially M^-1 is equal to the transposed Matrix

Hence why only 1 Mark. I have absolutely no idea if that correct though...

MM^T = 18MM^-1

M^T = 18 M^-1

M^-1 = 1/18 M^T

I am confusing myself over d now though aha. Thanks for the response 🙏

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#6

**Silurianwarrior1**)

I think this is correct?? Let me know.

It’s just playing around with the matrix identities.

So essentially M^-1 is equal to the transposed Matrix

Hence why only 1 Mark. I have absolutely no idea if that correct though...

**wbanner2001**)

1) How do you do 8c quickly if it is 1 mark and consequently 8d?

2) Why is my answer to 9c nothing like the show that?

Just take their fact and divide by then it's clear that

so obviously you now have being multiplied by which outputs the identity matrix... not much to say here other than realise that this necessarily means .

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(Original post by

9c. You need to get it in the form x+iy before you can isolate the real part like that. So, mupltiply top & bottom by the complex conjugate of the denominator.

**ghostwalker**)9c. You need to get it in the form x+iy before you can isolate the real part like that. So, mupltiply top & bottom by the complex conjugate of the denominator.

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For 9d I did this but got sin 2x = -4 which

is obviously invalid so can you see what I did wrong?

is obviously invalid so can you see what I did wrong?

(Original post by

9c. You need to get it in the form x+iy before you can isolate the real part like that. So, mupltiply top & bottom by the complex conjugate of the denominator.

**ghostwalker7842412**)9c. You need to get it in the form x+iy before you can isolate the real part like that. So, mupltiply top & bottom by the complex conjugate of the denominator.

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#9

(Original post by

Not correct. You cannot cancel matrices like that generally, so don't get into that habit, although it's premitted here since this matrix is I.

The fact that means that are pretty much inverses of each other. Not exactly though, because if they were then where but you already correctly determined it is , so we would obtain a contradiction in saying that.

Just take their fact and divide by then it's clear that

so obviously you now have being multiplied by which outputs the identity matrix... not much to say here other than realise that this necessarily means .

**RDKGames**)Not correct. You cannot cancel matrices like that generally, so don't get into that habit, although it's premitted here since this matrix is I.

The fact that means that are pretty much inverses of each other. Not exactly though, because if they were then where but you already correctly determined it is , so we would obtain a contradiction in saying that.

Just take their fact and divide by then it's clear that

so obviously you now have being multiplied by which outputs the identity matrix... not much to say here other than realise that this necessarily means .

Hence why I cancelled them out. My answer of M^T = K(M^-1) is what you achieved also...

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#10

(Original post by

You CAN cancel IDENTITY matrices...

Hence why I cancelled them out. My answer of M^T = K(M^-1) is what you achieved also...

**Silurianwarrior1**)You CAN cancel IDENTITY matrices...

Hence why I cancelled them out. My answer of M^T = K(M^-1) is what you achieved also...

does not mean .

You should take these properties more seriously by instead of putting a slash through , instead note that is such a matrix so that . Also, since we don't have commutativity, you need to pre-multiply or post-multiply by . Hence the correct practice to get into for matrices is as follows;

where at no point have I 'cancelled' out common matrices between both sides, and I have strictly pre-multiplied both sides by .

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#11

(Original post by

For 9d I did this but got sin 2x = -4 which

is obviously invalid so can you see what I did wrong?

**wbanner2001**)For 9d I did this but got sin 2x = -4 which

is obviously invalid so can you see what I did wrong?

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(Original post by

That's what I effectively said, but more importantly I told you to not get into the habit of cancelling out matrices between both sides. You cannot divide by a matrix and multiplication is not commutative.

does not mean .

You should take these properties more seriously by instead of putting a slash through , instead note that is such a matrix so that . Also, since we don't have commutativity, you need to pre-multiply or post-multiply by . Hence the correct practice to get into for matrices is as follows;

where at no point have I 'cancelled' out common matrices between both sides, and I have strictly pre-multiplied both sides by .

**RDKGames**)That's what I effectively said, but more importantly I told you to not get into the habit of cancelling out matrices between both sides. You cannot divide by a matrix and multiplication is not commutative.

does not mean .

You should take these properties more seriously by instead of putting a slash through , instead note that is such a matrix so that . Also, since we don't have commutativity, you need to pre-multiply or post-multiply by . Hence the correct practice to get into for matrices is as follows;

where at no point have I 'cancelled' out common matrices between both sides, and I have strictly pre-multiplied both sides by .

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(Original post by

I would suggest checking the formula you have for S - you've not posted its derivation, but I'd guess that's where the problem lies.

**ghostwalker**)I would suggest checking the formula you have for S - you've not posted its derivation, but I'd guess that's where the problem lies.

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#14

(Original post by

Can you see what I need to do for 9d?

**wbanner2001**)Can you see what I need to do for 9d?

Don't have time to look into this too much at the moment, but for 8d have you tried solving the following system?

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(Original post by

Don't have time to look into this too much at the moment, but for 8d have you tried solving the following system?

**RDKGames**)Don't have time to look into this too much at the moment, but for 8d have you tried solving the following system?

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#16

(Original post by

I had set up those three but the squares put me off... I will try again! Thanks

**wbanner2001**)I had set up those three but the squares put me off... I will try again! Thanks

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