Determine whether the statement below is . Justify the answer.
The columns of the standard matrix for a linear transformation from ℝ ⁿ to ℝ ᵐ are the images of the columns of the nn identity matrix.
Choose the correct answer below.
A. The statement is true. The standard matrix is the identity matrix in ℝ ⁿ
B. The statement is false. The standard matrix is the mn matrix whose jth column is the vector T(eⱼ) where eⱼ is the jth column whose entries are all 0.
C. The statement is false. The standard matrix only has the trivial solution.
D. The statement is true. The standard matrix is the mn matrix whose jth column is the vector T(eⱼ) where eⱼ is the jth column of the identity matrix in ℝ ⁿ