In Exercises mark each statement True or False. Justify
Chapter 1, Problem 22E(choose chapter or problem)
In Exercises 21 and 22, mark each statement True or False. Justify each answer.
a. Every matrix transformation is a linear transformation.
b. The codomain of the transformation \(\mathbf{x} \mapsto A \mathbf{x}\) is the set of all linear combinations of the columns of A.
c. If \(T: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}\) is a linear transformation and if c is in \(\mathbb{R}^{m}\), then a uniqueness question is "Is c in the range of T?"
d. A linear transformation preserves the operations of vector addition and scalar multiplication.
e. The superposition principle is a physical description of a linear transformation.
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