Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Step-by-step explanation:
a) If the given set of vectors does not span [tex]\mathbb{R}^{3}[/tex] , it means the number of linearly independent vectors are less than 3. So by adding one or more linearly independent vectors with respect to existing vectors, we can convert the set to basis and basis always spans vector space.
eg. [tex]S= \left \{ (1,0,0)^{T},(1,2,0)^{T} \right \}[/tex] this set does not span [tex]\mathbb{R}^{3}[/tex] . Since it has only two vectors and both vectors are linearly independent, so adding one linearly independent vector with respect to the vectors of S viz. (0,0,1)^{T} can span whole [tex]\mathbb{R}^{3} [/tex].
b) It is not possible. Since if a set of vectors is linearly dependent then after adding linearly independent vectors it will also linearly dependent i.e. addition of a linearly independent vector does not effect on the set.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
