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Is algebra in detective work?
Detectives have to prove their theories. Mathematics is one method of proving their case. Numbers don't lie.
Does maximizing the scalar multiplication in matrix chain multiplication exhibit optimal substructure?
I think so. Copy and paste method could be used to prove this. But this is only my opinion.
What method would you use to prove that segment UV is congruent to segment WV?
If V is the midpoint of the segment UW, then you would use the Definition of a Midpoint, which states that two congruent segments are created.
How can you prove that a constucted line is parallel to a given line?
The answer depends on the method used for constructing the second line. But since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer.
What is induction in math term mean?
It is a method of proving a statement for all values of a variable - usually for all integers. Often, the process is as follows: Prove the statement for n = 1 Assume that the statement is true for n = k and prove that, in that case, it must be true for n = k+1. Invoke the law of induction to assert that it is true for all [integer] values of n.
