Is Kernel of T a line or a point?

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Homework Help Overview

The discussion revolves around the kernel of a linear transformation T, specifically whether it represents a line or a point in the context of linear algebra.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the nature of the kernel of T, questioning whether it is a plane, line, or point. There are attempts to clarify the definition and properties of the kernel, with some participants seeking more information about the original problem and the calculations involved.

Discussion Status

The discussion is ongoing, with some participants providing insights into the geometric interpretation of the kernel. There is a recognition that the kernel is a subspace, but there is no consensus on its specific dimensionality or representation. Participants are actively questioning the validity of the provided kernel value and its implications.

Contextual Notes

There are indications that the original poster may not have provided sufficient information regarding the transformation T or the method used to determine the kernel, leading to confusion among participants.

judahs_lion
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Homework Statement



Linearly speaking the Kernel of T is a ?


Homework Equations



I solved kernel of T to equal {<-5,3,1>}

The Attempt at a Solution



So is Kernel of T is a plane?
 
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What is the exact question? The kernel of a transformation is a subspace.
 
You need to provide way more information. I have no idea what you're asking, what you did, what you mean, etc.
 
T(x,y,z) = (x+2y -z,2x+3y+z,4x+7y-z)
so Kernel T = (-5, 3, 1)

So geometrically speaking the kernel of T is a _______________?
 
That's not the kernel of T. How did you solve for the kernel?
 
judahs_lion said:
T(x,y,z) = (x+2y -z,2x+3y+z,4x+7y-z)
so Kernel T = (-5, 3, 1)

So geometrically speaking the kernel of T is a _______________?

<-5, 3, 1> is not the kernel, but it spans the kernel. What does this mean in terms of other vectors in the kernel?
 

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