Show that for the system (1.36) with D ≠ 0, Cramer’s Rule (1.38) does provide a solution....

Show that for the system (1.36) with D ≠ 0, Cramer’s Rule (1.38) does provide a solution. [Hint: It suffices to check the first equation of (1.36), since the others are similar. Show that after substitution from (1.38) it can be written Show that the left−hand side can be written as

Now interpret the coefficients of k1, k2, k3 as determinants expanded by minors,]