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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.1 Euclidean spaces Section 1.1 1. Write a three-column zero vector, and a three-column nonzero vector, and a five-column zero vector and a five-column nonzero vector. 2. Suppose that the buyer for a manufacturing plant must order different quantities of oil, paper, steel, and plastics. He will order 40 units of oil, 50 units of paper, 80 units of steel, and 20 units of plastics. Write the quantities in a single vector. 3. Suppose that a student's course marks for quiz 1, quiz 2, test 1, test 2, and the final exam are 70, 85, 80, 75, and 90, respectively. Write his marks as a column vector. 2 4. Let a = Find all z, y, z ER that a = b x-2y 2x - y and b-2 2z 5. a = I .2 y² (x-y 2 6. a ₁6² = ( ₂ ² ₂ ). . Find all x, y ER such that is a nonzero vector. 7. Let P(1, ²), Q(3, 4), Pi(4, 5), and Q1 (6, 1). Find all possible values of ER such that 4 PQ = P₁Q₁. -(₁) Find all z, y ER such that a = b. and b = 7. and b → 553
Transcribed Image Text:A.1 Euclidean spaces Section 1.1 1. Write a three-column zero vector, and a three-column nonzero vector, and a five-column zero vector and a five-column nonzero vector. 2. Suppose that the buyer for a manufacturing plant must order different quantities of oil, paper, steel, and plastics. He will order 40 units of oil, 50 units of paper, 80 units of steel, and 20 units of plastics. Write the quantities in a single vector. 3. Suppose that a student's course marks for quiz 1, quiz 2, test 1, test 2, and the final exam are 70, 85, 80, 75, and 90, respectively. Write his marks as a column vector. 2 4. Let a = Find all z, y, z ER that a = b x-2y 2x - y and b-2 2z 5. a = I .2 y² (x-y 2 6. a ₁6² = ( ₂ ² ₂ ). . Find all x, y ER such that is a nonzero vector. 7. Let P(1, ²), Q(3, 4), Pi(4, 5), and Q1 (6, 1). Find all possible values of ER such that 4 PQ = P₁Q₁. -(₁) Find all z, y ER such that a = b. and b = 7. and b → 553
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