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Unformatted text preview: MAE260 Lecture 8 Linear Algebra: Part I November 10, 2011 Fall 2011 MAE260 8–1 Matrices Some notations: – v ∈ R n : v is a ndimensional vector whose entries are all real. – A ∈ R n × m : A is a m by n matrix whose entries are all real – We can also define vectors and matrices in complex domain (and the textbook is written in this domain), but for now we will focus on real vectors and matrices for which we can easily talk about their geometric meanings. I assume that everyone is familiar with matrix addition and multipli cation – so, I will skip them. Your probably first encounter of matrices in the context of System of Linear Equations: – Example: Dad gives 1/10 of his income to his 1st kid and 1/6 to his 2nd kid, while Mon gives 1/9 of her income to the 1st kid and 1/8 to the 2nd one. Dad’s income = x D , Mom’s income = x M , 1st kid’s allowance = y 1 , and 2nd kid’s allowance = y 2 . Then, we have y 1 = 1 10 x D + 1 6 x M y 2 = 1 9 x D + 1 8 x M , which can be written as: y 1 y 2 = 1 10 1 6 1 9 1 8 x D x M – Two types of problems can be paused with the above representa tion. – Forward problem: for given x D and x M , find y 1 and y 2 ⇒ simply matrix multiplication November 10, 2011 Fall 2011 MAE260 8–2 – Backward problem: for given y 1 and y 2 , what is appropriate x D and x M ? ⇒ linear equation solving, which have interested many people and is still a research problem. – We will revisit linear equation solving in the later part. Another encounter of matrices: coordinate transformation and/or vector rotation....
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 Spring '12
 Park,SeungO&HanLimChoi
 Linear Algebra, Linear Equations, Invertible matrix

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