Let T R^5 rightarrow R^3 be a linear transformation whose null space.pdf
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The document discusses a linear transformation t from r^5 to r^3 with a null space of dimension three. According to a theorem on linear transformations, the dimension of the image of t is two. Geometrically, this means the image is a two-dimensional subspace, specifically a plane, within r^3.
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Let T R^5 rightarrow R^3 be a linear transformation whose null space.pdf
- 1. Let T: R^5 rightarrow R^3 be a linear transformation whose null space is a three dimensional subspace of R^5. What is the dimension of the image of T? Describe the image geometrically Is the image of T a subset of R^5 or R^3? Solution Theorem: If T::V->W is a linear transformation , then dim V = dim Null space T + dim Image T In the present case, dim V=5, dim Nullspace is 3 (given) So dim (Image T) (using the theorem ) is 2. Geometrically , Image of T is a two dimensional subspace (a plane) of R3 Image of T is a subspace (hence a subset of R3)