It costs a bakery $6 to bake a cake. If it sells on the first day, the bakery charges $15. If it sells on the second day, it charges $9. Otherwise, the cake is thrown out. The chance that a cake will sell on the first day is 65% and the chance that it will sell on the second day is 23%. How much profit (or loss) will the bakery make on each cake?
Determine all values of the constant a for which the following system has (a) no
solution, (b) an infinite number of solutions, and (c) a unique solution.
ax1 + x2 + x3 = 1,
x1 + ax2 + x3 = 1,
x1 + x2 + ax3 = 1.