Mathematics: Triangle abc is a right triangle point d is the midpoint of side ab and point e is the midpoint of side ac. the measure of angle ade is 68 degrees

Triangle abc is a right triangle point d is the

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sosick90501

20.02.2023

Mathematics

The problem lies with non-invertible matrices, i.e. those with determinant 0.

In fact, in order for to be a group, you need that:

is closed under multiplication. And it is, because the multiplication of two 2x2 matrices with rational coefficient is still a 2x2 matrix with rational coefficientsThere exists an element $e \in M$ such that Ae=eA

for all $A\in M$ . And again you have it,

is the matrix with 1 on the diagonal and 0 elsewhereEach element $A \in M$ must have an inverse $A' \in M$ such that AA'=A'A=e

, and this is where this example fails. If

isn't invertible (for example, pick the all-zeroes matrix), then you can't find a matrix $A' \in M$ such that AA'=A'A=e

So, this isn't a group

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Triangle abc is a right triangle point d is the midpoint of side ab and point e is the midpoint of side ac. the measure of angle ade is 68 degrees

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