Determine if the given set W is a subspace of the given vector space V. If so, find a possible basis for W and give the dimension of W. (a) V = M₂x2 (R), W = (b) V = M3×3 (R), W {(²-3² x = x² - y² x + y xy {A € M3x3 (R) AT = -A}, the set of all skew-symmetric 3 × 3 matrices with real coefficients : x, y ER (c) V = R₂(X), W = {(2a - 3b + 1) + (-2a + 5b)X + (2a + b)X²: a, b = R} (d) V = R4(X), W = {ao + a₁X + a₂X² + a3X³ + a₁X4 ao, a₁,..., an ER, ao + a₁ + a₂ + a3 + a₁ = 0} :
Determine if the given set W is a subspace of the given vector space V. If so, find a possible basis for W and give the dimension of W. (a) V = M₂x2 (R), W = (b) V = M3×3 (R), W {(²-3² x = x² - y² x + y xy {A € M3x3 (R) AT = -A}, the set of all skew-symmetric 3 × 3 matrices with real coefficients : x, y ER (c) V = R₂(X), W = {(2a - 3b + 1) + (-2a + 5b)X + (2a + b)X²: a, b = R} (d) V = R4(X), W = {ao + a₁X + a₂X² + a3X³ + a₁X4 ao, a₁,..., an ER, ao + a₁ + a₂ + a3 + a₁ = 0} :
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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