Which of the statements below is not true? A. The sum of products of vectors v_1

Question

Which of the statements below is not true? A. The sum of products of vectors v_1, ..., v_p by the scalars c_1, c_p, respectively, is called a linear combination of the given vectors with the given scalars as weights. B. A vector b in R^n can be written as a linear combination of v_1, ..., v_p if and only if the vector equation x_1v_1 + + x_pv_p = b has a solution. C. The zero vector in R^n cannot be written as a linear combination of any set of vectors in R^n. D. The set of all linear combinations of the vectors v_1, ...v_p, in R^n is called a subset of R^n spanned by v_1, .., v_p and denoted Span{v_1, , v_p}. E. b is in Span {v_1, v_p} if and only if the linear system with augmented matrix [v_1...v_p b] is consistent.

Explanation / Answer

(A) True

they ( v1,... vp) all are linearly dependent on the scalars

(B) True

A vector b is a linear combination only if the equation Ax = b has at least one solution

(C) true

a set containing the zero vector is not linearly independent

(D) True

(E) False

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