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.

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step-by-step explanation: