Let A be an m x n matrix with real number entries. Let N(A) be the null space of A, and let Col(A) be the vector space generated by the column vectors of A. Prove that Col(A) = N(AT).
Let A be an m x n matrix with real number entries. Let N(A) be the null space of A, and let Col(A) be the vector space generated by the column vectors of A. Prove that Col(A) = N(AT).
Let A be an m x n matrix with real number entries. Let N(A) be the null space of A, and let Col(A) be the vector space generated by the column vectors of A. Prove that Col(A) = N(AT).
Transcribed Image Text:Let A be an m × n matrix with real number entries. Let N(A) be the null space of A,
and let Col(A) be the vector space generated by the column vectors of A. Prove that
Col(A) = N(AT).
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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