Let T : R" → R" be a linear transformation defined by T(x) = Ax for some m x n matrix A. Assume that m > 1 and n > 1. If the rank of A is less than both m and n, then which of the following statements is false? Select one: O a. T is not one-to-one (not injective). O b. The inverse linear transformation T-1 exists. O c. The matrix A is not necessarily a square matrix. O d. T is not onto (not surjective).

Let T : R" → R" be a linear transformation defined by T(x) = Ax for some m x n matrix A. Assume that m > 1 and n > 1. If the rank of A is less than both m and n, then which of the following statements is false? Select one: O a. T is not one-to-one (not injective). O b. The inverse linear transformation T-1 exists. O c. The matrix A is not necessarily a square matrix. O d. T is not onto (not surjective).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let T : R" → R" be a linear transformation defined by T(x) = Ax for some m x n
matrix A. Assume that m > 1 and n > 1. If the rank of A is less than both m and
n, then which of the following statements is false?
Select one:
O a. T is not one-to-one (not injective).
O b. The inverse linear transformation T-1 exists.
O c. The matrix A is not necessarily a square matrix.
O d. T is not onto (not surjective).

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