Arizona State University (ASU) MAT343 Applied Linear Algebra Exam 2 Practice

In the equation \(Ax = b\), vector \(x\) plays a crucial role as it represents the unknown variables in the system of equations. When you express a system of linear equations in this form, \(A\) is typically a matrix containing the coefficients of those equations, \(x\) is the vector of variables whose values we want to determine, and \(b\) is a vector representing the outputs or constants from the equations.

The interpretation of \(x\) as the unknown variables is fundamental to solving linear systems. Solving for \(x\) involves finding the values that satisfy the equation, effectively allowing you to determine the relationship dictated by matrix \(A\) and vector \(b\).

While other statements may involve related concepts—outputs of the equations pertain to vector \(b\), constants correspond to certain fixed values seen in the equations, and vector \(x\) can be seen in the context of forming linear combinations of the columns of \(A\)—the precise role of \(x\) is that of representing the unknowns we are solving for. This clarifies its function in the matrix equation context.