Lecture 07.2 : Vector Spaces and Subspaces

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  1. Dr. Mervat Mikhail - FOE
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00:00 - introduction to vectors
15:17 - Vector spaces: when to say a system is a vector space?(10 conditions)
21:55 - famous examples for vector spaces
28:45 - Examples for non-vector spaces
40:22 - Subspaces (3 conditions)
43:29 - Example 1: ZX S.S. in R3
48:34 - important note about proof in math
50:00 - Example 2: {x1, x2, 1} S.S. in R3
51:19 - Example 3: {x1, x2}; x+2y = 1 S.S. in R2
52:41 - Example 4: {x1, x2}; x+2y = 0 S.S. in R2
57:00 - Example 5: {x, y}; x^2 + y^2 = 1 S.S in R2
58:11 - Example 6: {x, y}; x^2 + y^2 =< 1 S.S in R2
01:00:11 - Example 7: {x, y}; x=< 0, y=< 0(1st quadrant) S.S in R2
01:02:47 - Example 8: {x, y}; xy => 0{1st and 3rd quads.} S.S in R2
01:04:59 - Example 9: {x, xz, z} S.S in R3
01:09:24 - Recap

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