Which of the following statements is false?

a. R3 is a vector space

b. P2 is a vector space

C. M2x2 is a vector space

d. The set of all polynomials of degree 4 is a vector space

C. M2x2 is a vector space

Step-by-step explanation:

According to the definition, the each element in a vector spaces is a vector. So, 2*2 matrix cannot be element in a vector space since it is not even a vector.

The set of all ordered triples of real numbers is called 3-space, denoted R 3 ("R three"). See Figure ... Vectors in R 3 are called 3-vectors (because there are 3 components), and the geometric descriptions of addition and scalar multiplication given for 2-vectors also carry over to 3-vectors.

Since every polynomial of degree up to 2 is also a polynomial of degree up to 3, P2 is a subset of P3. And we already know that P2 is a vector space, so it is a subspace of P3.

With addition, the set of polynomials of degree 2 almost form a vector space, but there are some problem. The first one, is that the zero vector, i. e. the zero polynomial is not of degree 2 ... If you really need them to form a vector space, then you should consider the set of all polynomials of degree at most 2.