V is a vector space. Mark each statement True or False. Justify each answer. a. R^2 is a two-dimensional subspace of R^3.
b. The number of variables in the equation Ax D 0 equals the dimension of Nul A.
c. A vector space is infinite-dimensional if it is spanned by an infinite set.
d. If dimV D n and if S spans V, then S is a basis of V.
e. The only three-dimensional subspace of R^3 is R^3 itself.

Step-by-step explanation:

A) False ; R^2 is not a two dimensional subspace of R^3 because Vector R^2 will have 2 entries while vector R^3 has 3 entries

B) False : The number of variable in the equation is not equal to the Dimension because dim of Null A represents the number of free variables

C) False : This is because you can span R^3 with an infinite set of vectors but that doesn't make it infinite dimensional subspace

D) False : This is only possible when S has exactly n elements/vectors

E) True : Since R^3 is a three dimensional subspace it is spanned with 3 vectors whom are linearly independent

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^