Question

Suppose that x=(2,1,0,3),y=(3,−1,5,2), and z=(−1,0,2,1). Which of the following vectors are in span {x,y,z} ? (−2,3,−7,3) (2,3,−7,−3) (12,18,−42,18) (2,3,7,3) None of these Give your reasons

Answer 1

The vectors (−2,3,−7,3) and (2,3,7,3) are in the span of {x,y,z}.

Step-by-step explanation:

The vectors in span {x,y,z} are (−2,3,−7,3) and (2,3,7,3).

To determine if a vector is in the span of a set of vectors, we can row reduce the augmented matrix formed by the given vectors and the target vector. If the row-reduced form of the augmented matrix has any row where the augmented column is nonzero, then the target vector is not in the span of the given vectors. If every row in the row-reduced form has a zero in the augmented column, then the target vector is in the span of the given vectors.

In this case, let's row reduce the augmented matrix [x| V], where x is the given vectors and V is the target vector.