Let A ∈ Rm×n, B ∈ Rn×r, and C = AB. Show that (a) if the column vectors of B are linearly dependent, then the column vectors of C must be linearly dependent. (b) if the row vectors of A are linearly dependent, then the row vectors of C are linearly dependent.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.