MAT 2401 Linear Algebra 4.4 II Spanning Sets and Linear Independence

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Presentation transcript:

MAT 2401 Linear Algebra 4.4 II Spanning Sets and Linear Independence

HW WebAssign 4.4 Part II Written Homework

Review Linear Combination Spanning Set

Review: Example 0 (c)

Preview Linear Independent

Linear Independence

No one vector is a linear combination of the other vectors.

Example 6 Let S={(1,0,0), (0,0,2), (1,0,1)} Determine whether the set S is linearly independent or linearly dependent.

Example 7 Let S={(1,1,4), (1,0,3), (1,-1,0)} Determine whether the set S is linearly independent or linearly dependent.

Test

Written HW In this section, two related but different concepts are introduced: the spanning sets and linear independence.

Written HW Q1 : If S is a spanning set, does it imply that S is linearly independent?

Written HW Q1 : If S is a spanning set, does it imply that S is linearly independent? A1: No. Construct an counter example in R 2 Find S such that S spans R 2 and S is linearly dependent

Written HW Q2 : If S is linearly independent, does it imply that S is a spanning set?

Written HW Q2 : If S is linearly independent, does it imply that S is a spanning set? A2: No. Construct an counter example in R 3 Find S such that S is linearly independent and S does not span R 3