Let A be an m×n matrix. If these exist two distinct vectors v1 and v2 such that Av1=Av2 then there exists a non-zero vector, v, such as that Av= 0. Explain why this must be true. I'm a bit confused about this question, my first thought is that if the vectors always equal each other when multiplied by A, and the vectors are distinct (Assuming non-zero as well due to how the question is worded) then it must be that A is the reason they always equal and that A causes both sides to equal zero.

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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.