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Assignment4 Practice

Assignment4 Practice - Math 136 Practice Problems 4 1 For...

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Math 136 Practice Problems # 4 1. For each of the following systems of linear equations: i) Write the augmented matrix. ii) Row-reduce the augmented matrix into row echelon form. iii) Find the general solution of the system or explain why the system is inconsistent. a) x 1 + x 2 = - 7 2 x 1 + 4 x 2 + x 3 = - 16 x 1 + 2 x 2 + x 3 = 9 b) x 1 + x 2 + 2 x 3 + x 4 = 3 x 1 + 2 x 2 + 4 x 3 + 2 x 4 = 7 x 1 + x 4 = - 21 c) x 2 + x 3 = 2 x 1 + x 2 + x 3 = 3 2 x 1 + 3 x 2 + 3 x 3 = 9 d) 2 x 1 + x 2 - x 3 = 6 x 1 - 2 x 2 - 2 x 3 = 1 - x 1 + 12 x 2 + 8 x 3 = 7 e) z 2 - iz 3 = 1 + 3 i iz 1 - z 2 + ( - 1 + i ) z 3 = 1 + 2 i 2 z 1 + 2 iz 2 + (3 + 2 i ) z 3 = 4 1

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2 2. Let B = 1 1 0 1 , 2 0 0 2 , 0 2 - 1 1 . For each of the following vectors, either express it as a linear combination of the vectors of B or show that it is not a vector in span B . a) - 4 - 2 2 - 6 b) 6 0 0 3 3. Determine if the vector ~ b is in the span of the given set S . If it is, write ~ b
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Assignment4 Practice - Math 136 Practice Problems 4 1 For...

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