\begin{array}{c}

6 \cdot a \cdot y+4 \cdot x=2 \\

9 \cdot a \cdot x+6 \cdot y=5 \cdot b

\end{array} a. Write down the matrix of coefficients and the augmented matrix, and put both into echelon form.Which statement is true about the rank of the two matrices? (a) The rank of both matrices is always 2, independent of the values of a and b. (b) The rank of both matrices is always 1, independent of the values of a and b. (c) The rank of one matrix depends on the values of a and/or b, but the rank of the other matrix does not. (d) The ranks of both matrices depend on the values of a and/or b. b. Match the graphs to the cases: c. For what value(s) of a can we have no solution to the system of equations? a= a= d. Reminder: check the formatting instructions above.For what values of a and b do we have infinitely many solutions? Give your answer as the pair of coordinates (a, b).

(a, b) = e. In the case(s) where the choices of a and b mean there are infinitely many solutions, the variables x and y are related by an equation. Rearrange the equation to find the formula for y in terms of

y = f. Reminder: check the formatting instructions above.Finally, in the case where there is exactly one solution, find the formulas for x and y in terms of a and b.x =y =