a. Not every linear transformation from Rn to Rm is a matrix transformation. b. The col...

a. Not every linear transformation from Rⁿ to R^m is a matrix transformation.

b. The columns of the standard matrix for a linear transformation from Rn to Rm are the images of the columns of the n x n identity matrix.

c. The standard matrix of a linear transformation from R² to R² that reflects points through the horizontal axis, the vertical axis, or the origin has the form where a and dare .

d. A mapping is one-to-one if each vector in Rⁿ maps onto a unique vector in R^m.

e. If A is a 3 x 2 matrix, then the transformation cannot map R² onto R³.