Review sheet 1 - Length of vectors Cauchy-Schwarz...

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Here is a list of topics that may be covered on the first midterm, and problems to help you prepare. The intention is not that you will do all the problems, but that you will use this to identify the areas that you need to study and try to do some problems that you find difficult. For each homework assignment, I’ve listed a few odd-numbered problems from the textbook as well as the most useful homework problems. Homework 1: Topics: Systems of equations Vectors (addition, scalar mult.) Matrices (addition, scalar mult.) Most useful problems: B,C Odd problems: 12.6: 1, 5 Homework 2: Topics: Reduced Row Echelon Form/ Row Echelon Form Row reduction Matrix multiplication Scalar product/ dot product Transpose Most useful problems: B,D,E,F,G Odd problems: 12.4: 1; 12.7: 1; 12.8: 5 Homework 3: Topics: Geometric interpretation of vectors Orthogonality
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Unformatted text preview: Length of vectors Cauchy-Schwarz inequality Parametric form for lines and planes Most useful problems: D (answers to 1 are TFFT, 2 are TTFT) Odd problems: 12.4: 3, 5 Homework 4: Topics: Determinants Computing det using cofactor expansion Computing det using row reduction Inverses Linear transformations (you should be able to find matrices for projecting onto the axes, reflecting over the axes or y=x, and scaling- don’t need to know matrix for rotation or shear) Most useful problems: B,C,E Odd problems: 13.1: 3; 13.2: 1; 13.4: 3; 13.5: 1 Homework 5: Topics: Find inverses using row reduction Cramer’s Rule Linear Independence Span Rank Note: vector spaces, bases, and dimension will be saved for the second midterm. Most useful problems: B,C,E,F,G,H Odd problems: 13.7: 5; 13.8: 1; 14.2: 1; 14.3: 1...
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