Understanding Dot and Cross Product in Matrix Multiplication

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Homework Help Overview

The discussion revolves around the properties and applications of dot and cross products, particularly in the context of matrix multiplication. Participants explore the differences between these operations and their implications in mathematical contexts.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants attempt to explain why the dot product cannot be applied to three vectors simultaneously, while the cross product can. Questions are raised about the relationship between the dot product and matrix multiplication, and insights into how these concepts interrelate are sought.

Discussion Status

Some participants have provided clarifications regarding the nature of the dot and cross products, noting their scalar and vector results, respectively. There is an exploration of how the dot product aligns with matrix multiplication under specific conditions, although no consensus has been reached on all points discussed.

Contextual Notes

Participants are navigating the definitions and properties of vector operations within the constraints of their homework guidelines, which may limit the depth of exploration.

Pippa
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Explain, for example, why you can cross three vectors (two at a time, following the usual rules), but not dot three vectors. Do you see the dot product "in action" in matrix multiplication? What sort of insights can the dot product give when trying to comprehend matrix multiplication?
 
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the dot product is a scalar, the cross product is still a vector
 
The dot product coincides with matrix multiplication , when your matrices are 1xn and
nx1.
 
Thanks Guys :D
 
np-
basically you get a number if its 1xn and nx1 and another vector if its nx1 and nx1
 
Yep, a scalar dotted with a vector is undefined. Finally, something I can answer! :-)
 

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