MHB Equation of a Line Completing System with 3x - 2y = 8

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To create a system of equations with infinitely many solutions, the second equation must be identical to the first, which is 3x - 2y = 8. This means that any multiple of the original equation, such as 6x - 4y = 16, also works. However, simply repeating the original equation does not technically form a new system. The discussion highlights the importance of understanding that a valid system requires at least one equation to be a multiple of the other. Therefore, while the identical equation is correct, it does not fulfill the requirement for a distinct system.
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Q: Write an equation of a line that forms a system with the equation 3x - 2y = 8 that has infinitely solutions.
A: 3x - 2y = 8.
I believe this to be correct because it makes an identical line to one of her correct answers (6x - 4y = 16) and nowhere did it specify that it had to be new. Could you tell me my mistake?
 
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Did you really think that your teacher intended you to just copy what she had written? On a technical level repeating the same equation does NOT give a "system".
 
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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