UW Common Math 308 Section 2.3 - CHING FUNG CHUI Math 308...

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Current Score : 20 / 20 Due : Wednesday, October 21 2015 09:30 AM PDT 1. 1/1 points | Previous Answers HoltLinAlg1 2.3.004. Determine if the given vectors are linearly independent. 4 0 3 2 1 5 8 2 19 linearly independent linearly dependent x 1 u + x 2 v + x 3 w = 0, UW Common Math 308 Section 2.3 (Homework) CHING FUNG CHUI Math 308, section A, Fall 2015 Instructor: Hon Leung Lee TA WebAssign The due date for this assignment is past. Your work can be viewed below, but no changes can be made. Important! Before you view the answer key, decide whether or not you plan to request an extension. Your Instructor may not grant you an extension if you have viewed the answer key. Automatic extensions are not granted if you have viewed the answer key. Request Extension u = , v = , w = 3 3
2. 1/1 points | Previous Answers HoltLinAlg1 2.3.017. A matrix A is given. Determine if the homogeneous system (where x and 0 have the appropriate number of components) has any nontrivial solutions. A x = A = 1 2 1 3 2 1 2 0 5 A x = 0 has nontrivial solutions. A x = 0 has only the trivial solution. 0 2 3 3 0
3. 1/1 points | Previous Answers HoltLinAlg1 2.3.021. Determine by inspection (that is, with only minimal calculations) if the given vectors form a linearly dependent or linearly independent set. Justify your answer. Solution or Explanation Linearly dependent. Apply the theorem below. Suppose that is a set of vectors in R n . If then the set is linearly dependent. Linearly independent. The vectors are not scalar multiples of each other. Linearly dependent. Notice that u v + 3 w = 0 Linearly independent. If { u 1 , u 2 , , u m } is a set of vectors in R n and n < m , then the set is linearly independent. Linearly dependent. If { u 1 , u 2 , , u m } is a set of vectors in R n and n < m , then the set is linearly dependent. Linearly dependent. Notice that v = 2 u , so 2 u v = 0 { u 1 , u 2 , , u m } n < u = , v = , w = 3 1 6 5 1 7 . . m ,

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