Determine if the statement is true or false and justify your

Determine if the statement is true or false, and justify your answer. (a) The codomain of a linear transformation is a subset of the range. (b) All linear transformations T: R^n rightarrow R^m have the form T (x) = Ax for some matrix A.

Solution

Option A : (FALSE)

Co-Domain is equal to Range and not subset of Range

Option B : (TRUE)

Let A be an m × n matrix with real entries and define T : R ⁿ R ^m by T(x) = Ax.

Such a transformation is called a matrix transformation. Which implies, every linear transformation from R ⁿ to R ^m is a matrix transformation for some matrix A.