The rank-nullity theorem is a fundamental result in linear algebra that relates the dimensions of the kernel and the image of a linear transformation to the dimension of the domain. Specifically, it states that for a linear transformation from a vector space to another, the sum of the rank (the dimension of the image) and the nullity (the dimension of the kernel) equals the dimension of the domain. This theorem highlights key aspects of linear transformations and provides insights into their structure and properties.
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