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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.

Advanced Engineering Mathematics
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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a b Let 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 d a. 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.
Transcribed Image Text:a b Let 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 d a. 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.
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