MHB Using linear systems to solve problems (3)

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Rajah's earnings consist of an hourly wage and tips. In the first week, he worked 12 hours and earned a total of $117. In the second week, he worked 10 hours and earned $110, with tips equal to the previous week. By setting up a system of linear equations based on these earnings, one can solve for Rajah's hourly wage. The solution reveals the hourly wage Rajah earns from his work.
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Rajah earns an hourly wage plus tips. One week he worked 12 h and made a total of \$117. The next week he worked 10 h and earned the same amount in tips as the week before, for a total of \$110. What is Rajah's hourly wage?
 
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Only the slightest variation from the rental car problem.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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