Write the conclusion:
1 answer:
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For any arbitrary 2x2 matrices 
and 
, only one choice of exists to satisfy 
, which is the identity matrix.
There is no other matrix that would work unless we place some more restrictions on. One such restriction would be to ensure that is not singular, or its determinant is non-zero. Then this matrix has an inverse, and taking 
we'd get equality.
There is no other matrix that would work unless we place some more restrictions on
Answer:
The smallest value of p+q is 11
It happens when p = 6 and q = 5.
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Explanation:
Let's factor 180 in such a way that exactly one factor is a perfect square.
I'll ignore the trivial factor of 1.
Here are the possible factorizations we could go with:
180 = 4*45
180 = 9*20
180 = 36*5
Those factorizations then lead to the following
Then we have
p+q = 2+45 = 47
p+q = 3+20 = 23
p+q = 6+5 = 11
The smallest value of p+q is 11 and it happens when p = 6 and q = 5.
Side note: p+q is smallest when we go with the largest perfect square factor.