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4.20 Decide if R² is the direct sum of each W₁ and W₂. (a) W₁ = {(x) | x ≤ R}, W₂ = { (X) | XER} = ((1.15) | SER} (b) W₁ = {($) | s = R}, W₂ = {( (c) W₁ = R², W₂ = {0}

4.20 Decide if R² is the direct sum of each W₁ and W₂. (a) W₁ = {(x) | x ≤ R}, W₂ = { (X) | XER} = ((1.15) | SER} (b) W₁ = {($) | s = R}, W₂ = {( (c) W₁ = R², W₂ = {0}

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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Please do Exercise 4.20 part ABCDE and please show step by step and explain

Exercises ✓4.20 Decide if R² is the direct sum of each W₁ and W₂. = {(x) x € R}, W₂ = {(x) | XER} (₁) | SER}, W₂ = { ((1.1₁) | SER} S (a) W₁ = { (b) W₁ = { (c) W₁ = R², W₂ = {0} (d) W₁ = W₂ = {(t) |te R} (e) W₁ = { (1) + (3) | | x ≤ R}, W₂ = { ( (-¹) + (9) ¹4 [ y = R}
Transcribed Image Text:Exercises ✓4.20 Decide if R² is the direct sum of each W₁ and W₂. = {(x) x € R}, W₂ = {(x) | XER} (₁) | SER}, W₂ = { ((1.1₁) | SER} S (a) W₁ = { (b) W₁ = { (c) W₁ = R², W₂ = {0} (d) W₁ = W₂ = {(t) |te R} (e) W₁ = { (1) + (3) | | x ≤ R}, W₂ = { ( (-¹) + (9) ¹4 [ y = R}
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