a bLet M2 x2 be the vector space of all 2 x2 matrices, and define T: M2×2→M2×2 by T(A) = A+A', where A =c da. Show that T is a linear transformation.b. Let B be any element of M2 x2 such that BT = B. Find an A in M, x2 such that T(A) = B.c. Show that the range of T is the set of B in M2 x2 with the property that B' = B.d. Describe the kernel of T.

Answered: Image /qna-images/answer/c83c5520-c2d5-4b88-a149-235cda31ef85.jpg

a b Let M2 x2 be the vector space of all 2 ×2 matrices, and define T : M2 ×2→M2×2 by T(A) = A + A', where A = c d a. Show that T is a linear transformation. b. Let B be any element of M, x2 such that BT = B. Find an A in M2 x2 such that T(A) = B. c. Show that the range of T is the set of B in M,x2 with the property that BT = B. d. Describe the kernel of T.

a b Let M2 x2 be the vector space of all 2 ×2 matrices, and define T : M2 ×2→M2×2 by T(A) = A + A', where A = c d a. Show that T is a linear transformation. b. Let B be any element of M, x2 such that BT = B. Find an A in M2 x2 such that T(A) = B. c. Show that the range of T is the set of B in M,x2 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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