Solution Found!
In Example 3, we were given v1 = 1 1 1 1 , v2 = 0 1 3 1 R4 and constructed v3, v4 so
Chapter 3, Problem 2(choose chapter or problem)
In Example 3, we were given v1 = 1 1 1 1 , v2 = 0 1 3 1 R4 and constructed v3, v4 so that {v1, v2, v3, v4} gives a basis for R4. Here is an alternative construction: Consider the collection of vectors v1, v2, e1, e2, e3, e4; these certainly span R4. Now use the approach of Example 2 to find a basis {v1, v2, . . . }.
Questions & Answers
QUESTION:
In Example 3, we were given v1 = 1 1 1 1 , v2 = 0 1 3 1 R4 and constructed v3, v4 so that {v1, v2, v3, v4} gives a basis for R4. Here is an alternative construction: Consider the collection of vectors v1, v2, e1, e2, e3, e4; these certainly span R4. Now use the approach of Example 2 to find a basis {v1, v2, . . . }.
ANSWER:Step 1 of 2
Given,
We wish to find the additional vectors 
We consider the standard basis 
Now, we consider arbitrary constants 
