Determine whether w is in the span of the given vectors v1; v2; : : : vn

. If your answer is yes, write w as a linear combination of the vectors v1; v2; : : : vn and

enter the coefficients as entries of the matrix as instructed:

Determine whether w is in the span of the given ve

You dont have to use MATLAB. I just need to learn how to solve for w if w is a span of the given vectors. I

Determine whether w is in the span of the given vectors v1; v2; : : : vn

. If your answer is yes, write w as a linear combination of the vectors v1; v2; : : : vn and  enter the coefficients as entries of the matrix as instructed is given below

Explanation:

1.Vector to be in the span means means that it contain every element of said vector space it spans. So if a set of vectors A spans the vector space B, you can use linear combinations of the vectors in A to generate any vector in B because every vector in B is within the span of the vectors in A.

2.And thus v3 is in Span{v1, v2}. On the other hand, IF all solutions have c3 = 0, then for the same reason we may never write v3 as a sum of v1, v2 with weights. Thus, v3 is NOT in Span{v1, v2}.

3.In the theory of vector spaces, a set of vectors is said to be linearly dependent if at least one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be linearly independent.

4.Given a set of vectors, you can determine if they are linearly independent by writing the vectors as the columns of the matrix A, and solving Ax = 0. If there are any non-zero solutions, then the vectors are linearly dependent. If the only solution is x = 0, then they are linearly independent.

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