Trying to find a short way to solve two eqations inside a matrix.

[YehiaMedhat]

I think I hopefully could fi d the answer, but It took me long ti e until I found the solution, using matrix multiplication and addition then the comparison. I thi k there is a better way to solve faster, isn't there?!!

 

[Deleted member 4993]

View attachment 34327
I think I hopefully could fi d the answer, but It took me long ti e until I found the solution, using matrix multiplication and addition then the comparison. I thi k there is a better way to solve faster, isn't there?!!

Please show us what you have tried .

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this problem

 

[topsquark]

View attachment 34327
I think I hopefully could fi d the answer, but It took me long ti e until I found the solution, using matrix multiplication and addition then the comparison. I thi k there is a better way to solve faster, isn't there?!!

Unlikely. The only way I know of how to approach this is to multiply them out and solve for a and b. I didn't check your answer but, from your description, it sounds like you approached it the right way.

-Dan

 

[Steven G]

(A+B)^2 = (A+B)(A+B) = A^2 + AB + BA + B^2 = A^2 + B^2 under what condition? Just make sure that you satisfy that condition.

 

[YehiaMedhat]

(A+B)^2 = (A+B)(A+B) = A^2 + AB + BA + B^2 = A^2 + B^2 under what condition? Just make sure that you satisfy that condition.

Yeah, actually it's the same thing I have done. But it seems pretty long, so I had a question if anyone has any unordinary creative solution.

 

[Dr.Peterson]

Yeah, actually it's the same thing I have done. But it seems pretty long, so I had a question if anyone has any unordinary creative solution.

Please show your actual work, so we can see if you made it longer than it has to be.

 

[Steven G]

Exactly when does A^2 + AB + BA + B^2 = A^2 + B^2?

 

[YehiaMedhat]

Please show your actual work, so we can see if you made it longer than it has to be.

For r.h.s I calculated the A+B matrix, then squared it and for the l.h.s I calculated A square and B square, added them together and got the equations from which I got the solution.

 

[Dr.Peterson]

For r.h.s I calculated the A+B matrix, then squared it and for the l.h.s I calculated A square and B square, added them together and got the equations from which I got the solution.

Do you not see, from Steven G's hint, that you could calculate only AB and BA? That's a little less work.

 

[YehiaMedhat]

Do you not see, from Steven G's hint, that you could calculate only AB and BA? That's a little less work.

Ah, yesss, but I haven't noticed ?

 

[YehiaMedhat]

Exactly when does A^2 + AB + BA + B^2 = A^2 + B^2?

Thanks?

 

[Dr.Peterson]

Ah, yesss, but I haven't noticed ?

Can you see why we ask you to show your work from the beginning? We would have been able to give more direct advice, much more quickly, if you had followed the directions:

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[Steven G]

That is why, I asked two separate times when does A^2 + AB + BA + B^2 = A^2 + B^2?