lecture10

# lecture10 - achieve any total return desired between 10%...

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Math 006 (Lecture 10) Matrix Equations Example 1. Use matrix inverse to solve the system x 1 - x 2 + x 3 = 1 2 x 2 - x 3 = 1 2 x 1 + 3 x 2 = 1 Notes 1. Let A be an n × n invertible matrix, X and B be n × 1 column matrices, then the solution of the matrix equation AX = B is X = A - 1 B . Example 2. Use matrix inverse to solve the system x 1 - x 2 + x 3 = k 1 2 x 2 - x 3 = k 2 2 x 1 + 3 x 2 = k 3 1

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Applications Example 3. An investment advisor currently has two types of investment available for clients: a conservative investment A that pays 10%per year and an investment B of higher risk that pays 20% per year. Clients may divide their investments between the two to
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Unformatted text preview: achieve any total return desired between 10% and 20%. However, the higher the desired return, the higher the risk. How should each client listed in the table invest to achieve the indicated return? Client 1 Client 2 Client 3 Total investment \$20,000 \$50,000 \$10,000 Annual Return Desired \$2,400 \$ 7,500 1,300 Notes 2. We have three diﬀerent methods to solve a system of linear equations. They are 1. Method of Elimination 2. Gauss-Jordan Elimination 3. Inverse of a Matrix 2...
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## This note was uploaded on 09/04/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture10 - achieve any total return desired between 10%...

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