Let ax=b be any consistent system of linear equations, and let x1 be a fixed solution. show that every solution to the system can be written in form x=x1+x2, where x0 is a solution to ax=0. show that every matrix of this form is a solution.

The federal reserve controls certain interest rates in the united states. investors often try to speculate as to whether the federal reserve will raise or lower rates and by how much. suppose a company conducts extensive interviews with financial analysts, and as a result, predicts that "thefed" will increase rates by an average of 0.25 percentage points every six months for the forseeable future. which type of equation could be used to model the predicted interest rates over the next several years, assuming no other significant changes? a) a linear equation b) a quadratic equation c) a polynomial equation d) an exponential equation