Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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.

Sagot :

batolisis

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

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.