Consider an augmented matrix Au of a linear system: A := ( (1, 0, 2, 1) | (3, -4, 2, -1) |(2, 2 -4, 9, 7) ) : b := (1, - 1, t+4, t+3) : Au := (Alb) ; 1 3 2 0 -4 1 - 4 - 1 2 2 t+ 4 1 -1 7 t + 3 Find t for which (a) the system is inconsistent, (b) the system has a unique solution. (c) the system has infinitely many solutions. Explain your answers. (NOTE: here you can use any appropriate Maple command to find a row-echelon form of Au, you don't need to perform row reduction yourself) . Solution:Let u=(1,0,1) and v=(1, 1,0). Test the following 4 vectors to see which one is in the Span(u, v): w := (1, - 1, 2) : x := (4, 3, 1 ) : := (1, 1, 1) : z := (1, 2, - 1) : For those vectors which are in the span, provide a linear combination proving your conclusion. Solution