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Find all 2 x 2 matrices such that
The only way I could think of doing it is equating all matrix variables and solving simultaneously with my calculator. Is there an easier way to do this (cuz I sure couldn't do it by hand)!
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I believe you can use the Rational Canonical Form for this. Other than that, I see no other way besides what you mentioned.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Aren't there infinite solutions to this? Consider:
a and b are free variables, and so you can get as many such matrices as you want.
(Also ±I are two more.)
Why did the vector cross the road?
It wanted to be normal.
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Multiplying the first by d and the second by a and then equating → a[sup]2[/sup] = d[sup]2[/sup] ⇒ a = ±d.
Consider the following cases separately:
It turns out that case (ii) ⇒ a = d = 0 and becomes a special case of case (iv).
The complete solution:
Case (i) yields ±I, case (iii) yields the two middle sets and case (iv) yields the last set.
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Find all 2 x 2 matrices such that
The only way I could think of doing it is equating all matrix variables and solving simultaneously with my calculator. Is there an easier way to do this (cuz I sure couldn't do it by hand)!
Thanks for the help !
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