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Default Array formula needed

I want to perform an sumproduct type of function with on column of data (1 x
n) and the minimum value in each row of a 2 x n matrix. Is there a simple
formula that will allow me to do this. I know that I could create a new
column with the minimums or that I could brute force the math, I am just
hoping for something simple since I have to apply it a few hundred times.

Thanks
 
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