Exercise 8

What conditions must the constants, the $b$’s, satisfy so that each of these systems has a solution? Hint. Apply Gauss’s Method and see what happens to the right side.

• (a)  $\begin{array}{rcrcr}x&-&3y&=&b_{1}\\ 3x&+&y&=&b_{2}\\ x&+&7y&=&b_{3}\\ 2x&+&4y&=&b_{4}\end{array}$     (b)  $\begin{array}{rcrcrcr}x_{1}&+&2x_{2}&+&3x_{3}&=&b_{1}\\ 2x_{1}&+&5x_{2}&+&3x_{3}&=&b_{2}\\ x_{1}&&&+&8x_{3}&=&b_{3}\end{array}$