Triple scalar product question

AI Thread Summary
The triple scalar product is primarily applicable to 3D vectors and is used to determine the intersection of planes through their normals. It does not extend to solving matrices larger than 3x3 directly. The discussion highlights that while the triple scalar product can aid in understanding geometric relationships, it does not provide direct solutions to systems of equations or larger matrices. Clarification is needed on the intent behind using the triple scalar product in relation to higher-dimensional matrices. Ultimately, the triple scalar product serves specific geometric purposes rather than solving matrix equations.
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Homework Statement



Is it possible to use the triple scalar product to solve anything greater than a 3x3 matrix?

Homework Equations


Ax + By + Cz + D = 0


The Attempt at a Solution



In terms of planes, the triple scalar product can be used to determine if the NORMALS of the planes intersect at a point or on a line or in pairs.
But it doesn't necessarily give you the solution, does it?

So is it possible to use the triple scalar product to solve anything greater than a 3x3 matrix?
 
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It's not clear what you mean. You can solve a system of equations; you can solve an equation for a variable; you can solve a problem; etc. You don't solve a matrix. That's like saying you solve a number.
 

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