Let M2x2 be the vector space of all 2 x 2 matrices, and define -[: :} T: M2x2 → M2x2 by T(A) = A + AT , where A = a. Show that T is a linear transformation. b. Let B be any element of M2x2 such that BT = B. Find an A in M2x2 such that T (A) = B. c. Show that the range of T is the set of B in M2x2 with the property that BT = B. d. Describe the kernel of T.

Let M2x2 be the vector space of all 2 x 2 matrices, and define -[: :} T: M2x2 → M2x2 by T(A) = A + AT , where A = a. Show that T is a linear transformation. b. Let B be any element of M2x2 such that BT = B. Find an A in M2x2 such that T (A) = B. c. Show that the range of T is the set of B in M2x2 with the property that BT = B. d. Describe the kernel of T.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 16RQ

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