Let v1 v2 and v3 Does v1v2 v3 span R4 Why or why not Choose

Let v_1= v_2= and v_3= Does {v_1,v_2, v_3} span R^4? Why or why not? Choose the correct answer below. Yes. When the given vectors are written as the columns of a matrix A, A has a pivot position in every row. No. When the given vectors are written as the columns of a matrix A, A has a pivot position in only three rows. Yes. Any vector in R4 except the zero vector can be written as a linear combination of these three vectors. No. The set of given vectors spans a plane in R4. Any of the three vectors can be written as a linear combination of the other two.

Solution

The set {v1;v2;v3} does not span R4.Let v1,v2, and v3 be the columns of a matrix A. A has a pivot position in every column, then its rows will span R4. But there are only three rows in A, so there can be at most three pivot positions. So, The three vectors cannot span R4.

B