10. Let V = M2×2, W,(R) = {; ev : E V : a, b, с€R = {[°. ] ev : « W2 (R) = V : a €R} then prove that W1 and W2 are subspaces of V, and find the dimension of W1, W2, and W1NW2 respectively.
10. Let V = M2×2, W,(R) = {; ev : E V : a, b, с€R = {[°. ] ev : « W2 (R) = V : a €R} then prove that W1 and W2 are subspaces of V, and find the dimension of W1, W2, and W1NW2 respectively.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 31EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set...
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Question
Let V = M22,
W1(R) =
a b
b c
2 V : a; b; c 2 R
W2(R) =
0 a
?a 0
2 V : a 2 R
then prove that W1 and W2 are subspaces of V, and nd the dimension
of W1, W2, and W1
T
W2 respectively.
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