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1. Given vectors B = (2,–3),C=(6,9) in R² . Examine if they are linearly independent. 2. Given vectors X =(2,-3),W =(6,-9) in R°. Examine if they are linearly independent. 3. Given vectors A= (2,-3,1), B = (6,9,–1) in R’. Examine if they are linearly independent. 4. Given vectors A=(2,-3,1), B = (6,9,–1),C =(0,9,1) in R’. Examine if they are linearly independent. 5. Find constant k so that vectors B= (2,3),C =(3,k) in R² are linearly dependent.

1. Given vectors B = (2,–3),C=(6,9) in R² . Examine if they are linearly independent. 2. Given vectors X =(2,-3),W =(6,-9) in R°. Examine if they are linearly independent. 3. Given vectors A= (2,-3,1), B = (6,9,–1) in R’. Examine if they are linearly independent. 4. Given vectors A=(2,-3,1), B = (6,9,–1),C =(0,9,1) in R’. Examine if they are linearly independent. 5. Find constant k so that vectors B= (2,3),C =(3,k) in R² are linearly dependent.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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1. Given vectors B= (2,–3),C=(6,9) in R² . Examine if they are linearly independent. 2. Given vectors X =(2,-3),W =(6,-9) in R². Examine if they are linearly independent. 3. Given vectors A= (2,-3,1), B = (6,9,–1) in R’. Examine if they are linearly independent. 4. Given vectors A= (2,–3,1), B = (6,9,–1),C=(0,9,1) in R’. Examine if they are linearly independent. 5. Find constant k so that vectors B =(2,3),C=(3,k) in R are linearly dependent.
Transcribed Image Text:1. Given vectors B= (2,–3),C=(6,9) in R² . Examine if they are linearly independent. 2. Given vectors X =(2,-3),W =(6,-9) in R². Examine if they are linearly independent. 3. Given vectors A= (2,-3,1), B = (6,9,–1) in R’. Examine if they are linearly independent. 4. Given vectors A= (2,–3,1), B = (6,9,–1),C=(0,9,1) in R’. Examine if they are linearly independent. 5. Find constant k so that vectors B =(2,3),C=(3,k) in R are linearly dependent.
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