# CS-411 - Homework 0 (0%)

Linear Algebra Reminder. Due by: September 5, 2017

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• (A) Let: A =  1 2 3 , B =  4 5 6 , C =   − 1 1 3 , find:
1. 2A − B
2. ||A|| and the angle of A relative to the positive X axis
3. , a unit vector in the direction of A
4. the direction cosines of A
5. AB and BA
6. the angle between A and B
7. a vector which is perpendicular to A
8. A × B and B × A
9. a vector which is perpendicular to both A and B
10. the linear dependency between A, B, C
• (B) Let: A =  1 2 3 4  − 2 3 0 5  − 1 , B =  1 2 1 2 1  − 4 3  − 2 1 , C =  1 2 3 4 5 6  − 1 1 3 , find:
1. 2A − B
2. AB and BA
3. (AB)T and BTAT
4. |A| and |C| (note A-10)
5. the matrix (A, B, or C) in which the row vectors form an orthogonal set
6. A − 1 and B − 1 (note B-5)
• (C) Let: f(x)  = x2  + 3,   g(x,  y) = x2  + y2, find:
1. the first and second derivatives of f(x) with respect to x: f’(x), and f’’(x).
2. the partial derivatives: (g)/(x), and (g)/(y).

# Submission instructions

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