For a general linear transformation, about the most you can say are that the kernel and range are both subspaces (if they are not trivial). For different the kernel might be {(0,0,0)}, a line through (0,0,0), a plane through (0,0,0), or all of R3. Same for the range.eyehategod said:let T:R[tex]^{3}[/tex] [tex]\rightarrow[/tex] R[tex]^{3}[/tex] be a linear transformation.
how can i figure out a geometric description of the kernel and range of T. What do I have to look at?
A kernel in geometric description refers to the essential or fundamental part of a geometric shape or figure. It is the central or core component that defines the overall structure.
A kernel is often represented as a point or a set of points in geometric description. It can also be represented as a single line or curve that connects multiple points together.
The purpose of a kernel in geometric description is to provide a reference point for the rest of the shape. It helps to define the size, proportions, and spatial relationships within the shape.
Yes, a kernel can be modified in geometric description. By changing the position or properties of the kernel, the entire shape can be transformed or adjusted accordingly.
Some common examples of kernels in geometric description include the center point of a circle, the vertex of a triangle, and the origin point in a coordinate system.