MHB Troubleshooting: A=15-B, C=B+9, D=B+21

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The discussion revolves around solving a system of equations involving four variables: A, B, C, and D. The equations are derived from the relationships A=15-B, C=B+9, and D=B+21. After multiplying the equations by 3 and summing them, the total for A+B+C+D is found to be 78. Consequently, the average of the four numbers is calculated to be 19.5, confirming that the initial assumption of being above average is correct. The calculations validate the relationships between the variables and their average.
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View attachment 6392 I know that its well above average.

So I got A= 15-B, C=B+9 and D=B+21, but I think I made a mistake somewhere
 

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Let's denote the four numbers by $a$, $b$, $c$ and $d$. Then we have the following system.
\[
\left\{
\begin{aligned}
a+\frac13b+\frac13c+\frac13d=25\\
\frac13a+b+\frac13c+\frac13d=37\\
\frac13a+\frac13b+c+\frac13d=43\\
\frac13a+\frac13b+\frac13c+d=51\\
\end{aligned}
\right.
\]
Multiply each equation by 3 and add them. Recall that you need to find $\dfrac{a+b+c+d}{4}$.
 
6(A+B+C+D)=468

(A+B+C+D)=78

Average is 19.5?
 
You are right.
 
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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