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## Sagot :

From the problem statement, we have:

[tex]\[ \begin{align*} \text{Week 1:} & \quad 4t + 8b + 6g = 215 \\ \text{Week 2:} & \quad 3t + 5b + 4g = 145 \\ \text{Week 3:} & \quad 4t + 6b + 4g = 170 \end{align*} \][/tex]

These can be written in matrix form as:

[tex]\[ \begin{pmatrix} 4 & 8 & 6 \\ 3 & 5 & 4 \\ 4 & 6 & 4 \end{pmatrix} \begin{pmatrix} t \\ b \\ g \end{pmatrix} = \begin{pmatrix} 215 \\ 145 \\ 170 \end{pmatrix} \][/tex]

In this matrix equation, the matrix on the left-hand side represents the number of hours Suzie worked at each job each week, and the column vector represents her hourly wages. The right-hand side column vector represents the total earnings for each week.

Thus, the matrix equation is:

[tex]\[ \begin{pmatrix} 4 & 8 & 6 \\ 3 & 5 & 4 \\ 4 & 6 & 4 \end{pmatrix} \begin{pmatrix} t \\ b \\ g \end{pmatrix} = \begin{pmatrix} 215 \\ 145 \\ 170 \end{pmatrix} \][/tex]

Solving this system of linear equations will reveal the hourly wages [tex]\( t \)[/tex], [tex]\( b \)[/tex], and [tex]\( g \)[/tex]. The solution for these hourly wages is:

[tex]\[ t = 15.0, \quad b = 10.0, \quad g = 12.5 \][/tex]