1.41.5 - Homework 2 - Solutions 1.4 Problem 1 1. TRUE. Use...

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Homework 2 - Solutions 1.4 Problem 1 1. TRUE. Use the trivial linear combinations, taking all constants to be zero. 2. FALSE. By convention, span( )= { 0 } . 3. TRUE. See Theorem 1.5. 4. FALSE. Only multiplication by nonzero constants is allowed. 5. TRUE. 6. FALSE. See the system of equations in Example 2 of this section. 1.4 Problem 2b See example 1 of this section. 1.4 Problem 4b See example 2 of this section. 1.4 Problem 10 The span of { M 1 ,M 2 3 } consists of linear combinations of these matrices. LEt us consider an arbitrary linear combination: aM 1 + bM 2 + cM 3 = ± ac cb ² Since this is the most general 2 × 2 symmetric matrix, we see that the span of these three matrices must be all symmetric 2 × 2 matrices. 1.4 Problem 15 See class notes - this example was worked out in class. 1.5 Problem 1 1. FALSE. Consider the set { (1 , 0) , (1 , 1) , (2 , 2) } . 2. TRUE. 3. FALSE. This is a point of convention. If we assume to be independent, then taking the union of an independent set S with the empty set will keep S ∪∅ = S independent.
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1.41.5 - Homework 2 - Solutions 1.4 Problem 1 1. TRUE. Use...

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