MHB Troubleshooting (b), (c) & (e): Seeking Assistance

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The discussion focuses on troubleshooting parts (b), (c), and (e) of a problem related to the dot product. For part (b), participants are encouraged to write out the dot product formula and compare it with the right-hand side (RHS) to draw conclusions. In part (c), a similar approach is suggested, emphasizing the importance of analyzing the dot product formulas. Part (e) prompts a geometric interpretation, with advice to visualize examples to enhance understanding. The conversation highlights the need for clarity on geometric reasoning and the relationship between vectors and their negatives.
Joe20
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I have some difficulties answering part (b), (c) and (e).

Help is appreciated.
 

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(b) If you write out the formula for the dot product, what do you get? Now compare that with the RHS. What can you conclude?

(c) Again, I would write out the formulae for the dot products. What can you conclude?

(e) I would think about this one geometrically. Try drawing a few examples and see what you come up with.
 
Ackbach said:
(b) If you write out the formula for the dot product, what do you get? Now compare that with the RHS. What can you conclude?

(c) Again, I would write out the formulae for the dot products. What can you conclude?

(e) I would think about this one geometrically. Try drawing a few examples and see what you come up with.
Hi Ackbach,

Thanks for the advice. I am not very sure what is meant by thinking it geometrically and drawing a few examples in part (e). Would further advice on this. Thanks.
 
Alexis87 said:
Hi Ackbach,

Thanks for the advice. I am not very sure what is meant by thinking it geometrically and drawing a few examples in part (e). Would further advice on this. Thanks.

Well, here's another hint: $\mathbf{a}-\mathbf{b}=\mathbf{a}+(-\mathbf{b})$. So, comparing $\mathbf{a}+\mathbf{b}$ with $\mathbf{a}+(-\mathbf{b})$ gives you some information about what's going on. Geometrically, how does $\mathbf{b}$ compare with $-\mathbf{b}?$
 
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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