Gl (n, r), the set of invertible nxn matrices with real entries, is a group under matrix multiplication. determine if the nxn matrices with determinant -1 or 1 is a subgroup. if not, which property does not hold?

Let

The subset S is a subgroup of GL(n,R) if satisfies:

1. The identity matrix belong to S.

2. If A and B are in S then AB is in S.

3. If A is belong to S then belongs to S.

Let's see if S satisfies these conditions.

1.  We know that , then .

2. Let A and B in S.

Then AB is in S.

3. Let , , then .

Since S satisfies all conditions then S is a subgroup of GL(n,R).

x = 23.78

step-by-step explanation:

answer: the sun

explanation:

water cycle describes the evaporation of water from earth's surface, formation of clouds and precipitation water back onto the surface of earth. seventy percent of the earth is covered with water in the form of seas and oceans. the heat of the sun causes the evaporation of water from the surface of the ocean. the water vapors rise and condense to form water droplets. the collection of these water droplets form clouds which rain down again.

the evaporation of the oceans surface water as part of the water cycle is caused by the sun