試題詳解

複選題
10. (5%) Please pick the statements below that are true.
(A) The rank of the coefficient mnatrix of a consistent system of linear equations is equal to the ariables in the genera number of basic varia ral solution of the system.
(B) The matrix-vector product of an m X n matrix A and a' vector in Rⁿ is a linear combination of the columns of A.
(C) A subset of Rⁿ containing fewer than n vectors must be linearly independent.
(D) If S₁ and S₂ are finite subsets of R" having equal spans, then S₁and S₂ contain the same number of vectors.
(E) If the columns of an n X n matrix A for a generating set of Rⁿ, then the reduced row echelon form of A is In.