Answer:
b. set of real numbers R Superscript m is completely determined by its effect on the columns of the n times n identity matrix.
Explanation:
A linear transformation T can be defined as a set of real numbers Rn → Rm is completely determined by its effect on columns of the n × n identity matrix because:
1. The standard matrice's column for the purpose of linear transformation from row Rn to Rm can be termed as the images of columns of the given n x n identity matrix.
2. The standard matrice's column is the basis vector in row Rn. As we know that we can express any vector as a linear combination of these and T is expressed as a linear transformation.
Hence, the true option is (b)