Suppose that a2 = 0 for some matrix a. prove that the only possible eigenvalues of a are then 0.

The eigenvector of A is not equal to zero, then we can say λ or λ = 0. Therefore,  the only possible eigenvalues of A are 0.

Step-by-step explanation:

If we assume that λ is the eigenvalue of the matrix A and the eigenvector of the matrix A is ⁻ˣ. Therefore:

For

we have:

⁻0 = [⁰₀⁰₀][⁻ˣ] = *[⁻ˣ] = Aλ[⁻ˣ] = λ[⁻ˣ]

In the expression above, ⁻ˣ is not equal to zero, then λ = 0 or  λ is = 0. This shows that the only possible eigenvalues of A are zero '0'

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!