Description
- Exercise 4.1 Questions 2, 4 – write systems of equations in matrix form
- Exercise 4.2 Questions 1 b and d, 2, 4 a and d, 6 e – adding and multiplying matrices; using the summation sign
- Exercise 4.5 Questions 1 b and d, 2, 3 b and d – special matrices
- Exercise 4.6 Questions 2 and 4 – transpose
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Explanation & Answer
See for #4.1, #4.2 and #4.5
Exercise 4.1
2. Rewrite the market model (3.12) in the format of (4.1) with variables arranged in the
following order 𝑄𝑑1 , 𝑄𝑠1 , 𝑄𝑑2 , 𝑄𝑠2 , 𝑃1 , 𝑃2 . Write out the coefficient matrix, the variable
vector, and the constant vector.
Solution
Equation (3.1) is given as:
𝑄𝑑1 − 𝑄𝑠1 = 0
𝑄𝑑1 = 𝑎0 + 𝑎1 𝑃1 + 𝑎2 𝑃2
𝑄𝑠1 = 𝑏0 + 𝑏1 𝑃1 + 𝑏2 𝑃2
𝑄𝑑2 − 𝑄𝑠2 = 0
𝑄𝑑2 = 𝛼0 + 𝛼1 𝑃1 + 𝛼2 𝑃2
𝑄𝑠2 = 𝛽0 + 𝛽1 𝑃1 + 𝛽2 𝑃2
In the form of equation (4.1), equation (3.12) can be written as
𝑄𝑑1 − 𝑄𝑠1 = 0
𝑄𝑑1 − 𝑎1 𝑃1 − 𝑎2 𝑃2 = 𝑎0
𝑄𝑠1 − 𝑏1 𝑃1 − 𝑏2 𝑃2 = 𝑏0
𝑄𝑑2 − 𝑄𝑠2 = 0
𝑄𝑑2 − 𝛼1 𝑃1 − 𝛼2 𝑃2 = 𝛼0
𝑄𝑠2 − 𝛽1 𝑃1 − 𝛽2 𝑃2 = 𝛽0
𝑄𝑑1 − 𝑄𝑠1 + 0𝑄𝑑2 + 0𝑄𝑠2 + 0𝑃1 + 0𝑃2 = 0
𝑄𝑑1 + 0𝑄𝑠1 + 0𝑄𝑑2 + 0𝑄𝑠2 − 𝑎1 𝑃1 − 𝑎2 𝑃2 = 𝑎0
0𝑄𝑑1 + 𝑄𝑠1 + 0𝑄𝑑2 + 0𝑄𝑠2 − 𝑏1 𝑃1 − 𝑏2 𝑃2 = 𝑏0
0𝑄𝑑1 + 0𝑄𝑠1 + 𝑄𝑑2 − 𝑄𝑠2 + 0𝑃1 + 0𝑃2 = 0
0𝑄𝑑1 + 0𝑄𝑠1 + 𝑄𝑑2 + 0𝑄𝑠2 − 𝛼1 𝑃1 − 𝛼2 𝑃2 = 𝛼0
0𝑄𝑑1 + 0𝑄𝑠1 + 0𝑄𝑑2 + 𝑄𝑠2 − �...
Review
Review
