Finish the following definitions A subspace of Rn Is any set

Finish the following definitions A subspace of R^n Is any set H in R^n that satisfies the following properties... A basis for a subspace H of R^n Is a set of vectors in H that... The column space of a matrix A Is The null space of a matrix A is

Solution

d)  Null Space of a Matrix is a valid Subspace.

c) the column space C(A) of a matrix A (sometimes called the range of a matrix)

a) a subspace of Rⁿ is any set H in Rⁿ that satisfies the following properties

1 the zero vector 0 should be in it

2 H must be closed under addition . this means, if u and v are vector in H , then their sum u+v must be in it

3 H must be closed under scalar multiplication . this means if u is a vector in H and C is any scalar . then product CU must be in H