Let v be the vector space of all 2×2 matrices with real entries. let h be the set of all 2×2 idempotent matrices with real entries. is h a subspace of the vector space v? does h contain the zero vector of v?

Remember, a set is a subspace of the vector space V if:

.

1. Observe that

, where is the null matrix .

Then

2. Consider two matrices A and B such that in H

Observe that .

Then,

Then H is not a subspace of V

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.