Student 999
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How do you solve question 2ii and 2iii?
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Student 999
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I’ve tried to multiply out and equate but it doesn’t work
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mqb2766
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(Original post by Student 999)
I’ve tried to multiply out and equate but it doesn’t work
Can you upload what you've tried for ii)?
For c) just expand and use the B - B inverse .
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Student 999
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(Original post by mqb2766)
Can you upload what you've tried for ii)?
For c) just expand and use the B - B inverse .
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mqb2766
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Your B inverse is incorrect. How did you get it?
the formula is well known
https://www.mathsisfun.com/algebra/matrix-inverse.html

A quick check is B*B^(-1) should be the identity matrix.
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Student 999
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(Original post by mqb2766)
Your B inverse is incorrect. How did you get it?
the formula is well known
https://www.mathsisfun.com/algebra/matrix-inverse.html

A quick check is B*B^(-1) should be the identity matrix.
I’m sure my B^(-1) is correct anyhow if I were to use the identity matrix then it’ll leave me with A= the a 0 0 b which cant be possible since 1 doesn’t equal 0.

The best way for me to understand is if you posted your working out
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mqb2766
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(Original post by Student 999)
I’m sure my B^(-1) is correct anyhow if I were to use the identity matrix then it’ll leave me with A= the a 0 0 b which cant be possible since 1 doesn’t equal 0.

The best way for me to understand is if you posted your working out
Your b and c terms are wrong in B^(-1). Check your notes / website and if you want some help, please upload your calculations. Forum rules are that we dont give answers.
You can verify by
B*B^(-1) = B^(-1)*B = I
the identity matrix. This has no relation to A. Again, it's covered in your notes / website
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Student 999
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(Original post by mqb2766)
Your b and c terms are wrong in B^(-1). Check your notes / website and if you want some help, please upload your calculations. Forum rules are that we dont give answers.
You can verify by
B*B^(-1) = B^(-1)*B = I
the identity matrix. This has no relation to A. Again, it's covered in your notes /
I got a=1 b=3 but what should the wavelength symbol equal to as it does not matter what value I put it as
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davros
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(Original post by Student 999)
I got a=1 b=3 but what should the wavelength symbol equal to as it does not matter what value I put it as
I agree with a = 1 and b = 3. Unless I've made a mistake too, lambda (\lambda) can be any non-zero value since the result appears to be independent of lambda. If it were necessary to choose a value you could take lambda = 1 for simplicity - it does not affect the remaining parts of the question.
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Student 999
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On question 4 of 2 where I’m supposed to find A^100

So far I’ve got (1 0)
(? 3^100)

I understand that there is a sequence for ‘?’ however I don’t know how to express it as the sequence is 1,4,12,40 where it is adding 3^n to the previous value
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ghostwalker
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(Original post by Student 999)
On question 4 of 2 where I’m supposed to find A^100

So far I’ve got (1 0)
(? 3^100)

I understand that there is a sequence for ‘?’ however I don’t know how to express it as the sequence is 1,4,12,40 where it is adding 3^n to the previous value
You shouldn't be arriving at a sequence. Post your working.

You need to use part (ii) and a generalisation of part (iii) for this last part.

(Agree with others regarding a=1,b=3, lambda = anything non-zero)
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Student 999
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(Original post by ghostwalker)
you shouldn't be arriving at a sequence. Post your working.

You need to use part (ii) and a generalisation of part (iii) for this last part.

(agree with others regarding a=1,b=3, lambda = anything non-zero)
a= (1 0)
(1 3)

a^2=(1 0)
(4 9)

a^3=(1 0)
(12 27)

a^4=(1 0)
(40 81)
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mqb2766
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(Original post by Student 999)
a= (1 0)
(1 3)

a^2=(1 0)
(4 9)

a^3=(1 0)
(12 27)

a^4=(1 0)
(40 81)
You need part iii) to relate
[[a 0],[0,b]]^100
to A^100.

You've done it when its squared, what is the result when you raise it to the power of 100?
Then how can you reformulated the equation to get
A^100 = ....
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Student 999
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(Original post by mqb2766)
You need part iii) to relate
[[a 0],[0,b]]^100
to A^100.

You've done it when its squared, what is the result when you raise it to the power of 100?
Then how can you reformulated the equation to get
A^100 = ....
A^100

=(1 0)
( 3^100)

I’m stuck on finding c
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mqb2766
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(Original post by Student 999)
A^100

=(1 0)
( 3^100)

I’m stuck on finding c
The is not A^100. It's the diagonal matrix raised to 100.
Use iii) to express
A^2 =...
In terms of the diagonal matrix squared, then do the same when it's raised to the 100th power.
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Student 999
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(Original post by mqb2766)
The is not A^100. It's the diagonal matrix raised to 100.
Use iii) to express
A^2 =...
In terms of the diagonal matrix squared, then do the same when it's raised to the 100th power.
Using iii. A^2=B^(-1)A^2B

I don’t see how that will help
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mqb2766
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(Original post by Student 999)
Using iii. A^2=B^(-1)A^2B

I don’t see how that will help
Calling the diagonal matrix D (part ii, right hand side), you have (part iii):
D^2 = B^(-1)*A^2*B
Rearrange to get an expression for
A^2 = ...
You need to "invert" the Bs and get them over the other side and combine with the D^2.
Now do the same to get an expression for A^100 in terms of Bs and D^100.

It helps because you know B, B^(-1) and D^100 and you have to determine A^100.
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