Consider the linear system Ax =b for a given constant vector b. Determine whether the following statement is true: ”If this system has a unique solution, then the system Ax = c also has a unique solution for any other constant vector c.” (Assume that A, x, b, and c are all of compatible sizes.) Explain if true/false.

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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.