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/sci/ - Science & Math

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14999464 No.14999464 [Reply] [Original]

how to solve Ax=7x, where A is a 3x3 matrix and I want all possible solutions?

>> No.14999468

>>14999464
kek what a retard

>> No.14999469

>>14999468
pls help anon my deadline is soon :(

>> No.14999473

>>14999469
What have you tried?

>> No.14999476

>>14999473
I dont even know how to write this out. I have earlier only had assignments where I need to solve Ax=b but Ax=n*x is new to me

>> No.14999478

Subtract 7 from every element on the main diagonal of A and invert the resulting matrix.

>> No.14999479

>>14999464
Divide by x on both sides. This gives you A = 7. But since A is a matrix, you'll have to use a theorem of matrix expansion, which gives you a 3x3 matrix of only 7s.

>> No.14999481

Try writing A as a scalar matrix which satisfies the equation. Then you can find the similar matrices.

>> No.14999483
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14999483

>>14999479
but I already now matrix A is pic related
wtf

>> No.14999491

>>14999476
At least you are not the most retarde person in the thread. You want a matrix A such that right multiplying by A is equivalent to multiplying by 7.
Can you think of such a matrix?
Can you think of a matrix A such that right multiplying by A is equivalent to multiplying by 1?

>> No.14999494

>>14999483
You could have included this in the first post anon.
Simply replace 7 by 7*I and solve normally then.

>> No.14999498

>>14999483
The exercise is wrong then. Complain to your teacher.

>> No.14999506

Ax = 7x
Ax = 7*Ex , where E is the identity matrix - you can easily check that this is equivalent to multiplying every element of the vector by 7
Ax - 7*Ex = 0
(A - 7E)x = 0
Solve this equation (compute ker(A-7E))

>> No.14999508

>>14999494
Ok. Is it better to use Gaussian elimination for it or is there simpler way to do it?

>> No.14999515

>>14999508
Use Gaussian elimination. It becomes (A - 7*I)x = 0 as the other anon said.

>> No.14999517
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14999517

>>14999515
is this the correct form?

>> No.14999534

>>14999517
7I is the identity matrix multiplied by 7. I.e. a matrix with 7s in the main diagonal and 0s everywhere else.
Let C = A-7I and solve Cx = 0.
You know how to solve this, it’s Ax=b with A=C and b=0.

>> No.14999539

>>14999534
oh thank you anon so much

>> No.14999550
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14999550

>>14999534
I am not sure if the solution should be 0 for everything tho..

In the question they said that x should be in the form of pic rel

>> No.14999568

>>14999464
lol, this is literally an eigenvalue problem that is already half solved

>> No.14999620

>>14999568
well how the fuck can you tell me please anon?

>> No.14999662

>>14999464
Are you trying to solve for x? What's the rest of the equation/problem?

>> No.14999728

>>14999620

https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

>> No.14999730

>>14999464
>>>14999718
might be of some use.

>> No.14999734

>>14999728
nta, but this will probably be helpful as well.

>> No.14999764

>Baby math post
>24 replies
You disappoint me /sci/

>> No.14999766

>>14999764
the best way to deal with it is to answer the question before too many replies accumulate I imagine. it would be nice if these stayed in /sqt/ but what can be done really