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Question 2 over a field K. Let Mn(K) denotes the vector space of n x n matrices (a) Let U and V be the subspaces of V = M3(K) defined by U = {A Є M3(K)|A = A}, W = {A = M3(K)|A² = -A} where At denotes the transpose of A. Prove that V = U + W if K = R and prove that V U W if K = F2.

Question 2 over a field K. Let Mn(K) denotes the vector space of n x n matrices (a) Let U and V be the subspaces of V = M3(K) defined by U = {A Є M3(K)|A = A}, W = {A = M3(K)|A² = -A} where At denotes the transpose of A. Prove that V = U + W if K = R and prove that V U W if K = F2.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 5E
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Question 2 over a field K. Let Mn(K) denotes the vector space of n x n matrices
Transcribed Image Text:Question 2 over a field K. Let Mn(K) denotes the vector space of n x n matrices
(a) Let U and V be the subspaces of V = M3(K) defined by U = {A Є M3(K)|A = A}, W = {A = M3(K)|A² = -A} where At denotes the transpose of A. Prove that V = U + W if K = R and prove that V U W if K = F2.
Transcribed Image Text:(a) Let U and V be the subspaces of V = M3(K) defined by U = {A Є M3(K)|A = A}, W = {A = M3(K)|A² = -A} where At denotes the transpose of A. Prove that V = U + W if K = R and prove that V U W if K = F2.
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