Question

V is a vector space. Mark each statement True or False. Justify each answer.

Answer 1

Answer:

• False
• False
• False
• False
• True

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