Solution Found!
Decide whether the following sets of vectors give a basis for the indicated space. a
Chapter 3, Problem 3(choose chapter or problem)
Decide whether the following sets of vectors give a basis for the indicated space.
a. \(\{(1,2,1),(2,4,5),(1,2,3)\} ; \mathbb{R}^3\)
b. \(\{(1,0,1),(1,2,4),(2,2,5),(2,2,-1)\} ; \mathbb R^3\)
c. \(\{(1,0,2,3),(0,1,1,1),(1,1,4,4)\} ; \mathbb{R}^4\)
d. \(\{(1,0,2,3),(0,1,1,1),(1,1,4,4),(2,-2,1,2)\} ; \mathbb{R}^4\)
Questions & Answers
QUESTION:
Decide whether the following sets of vectors give a basis for the indicated space.
a. \(\{(1,2,1),(2,4,5),(1,2,3)\} ; \mathbb{R}^3\)
b. \(\{(1,0,1),(1,2,4),(2,2,5),(2,2,-1)\} ; \mathbb R^3\)
c. \(\{(1,0,2,3),(0,1,1,1),(1,1,4,4)\} ; \mathbb{R}^4\)
d. \(\{(1,0,2,3),(0,1,1,1),(1,1,4,4),(2,-2,1,2)\} ; \mathbb{R}^4\)
ANSWER:Step 1 of 4
(a). Given set of vectors is
To determine whether V is basis for 
Let us consider the matrix
To find if the given set is linearly independent or not, we will solve the equation 
The row reduced echelon form of the augmented matrix is
Since the solution of the equation 