gibson:teaching:spring-2016:math445:lab5
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gibson:teaching:spring-2016:math445:lab5 [2016/02/15 10:34] gibson |
gibson:teaching:spring-2016:math445:lab5 [2016/02/18 08:36] (current) gibson |
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| - | **Problem 2:** If $F$ is a temperature in Farenheit, then $C = \frac{5}{9}(F-32)$ is the same temperature in Celsius. Write a function ''farenheit2celsius'' that takes a Celsius temperature as input, converts it to Celsius, prints a statement of the form ''20 Farenheit is -6.6667 Celsius.'', and returns the Celsius value as its output. | + | **Problem 2:** If $F$ is a temperature in Farenheit, then $C = \frac{5}{9}(F-32)$ is the same temperature in Celsius. Write a function ''farenheit2celsius'' that takes a Farenheit temperature as input, converts it to Celsius, prints a statement of the form ''20 Farenheit is -6.6667 Celsius.'', and returns the Celsius value as its output. |
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| \begin{equation*} | \begin{equation*} | ||
| - | \text{deviation}(x) = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \bar{X})^2} | + | \text{deviation}(x) = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \bar{X})^2} |
| \end{equation*} | \end{equation*} | ||
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| - | **Problem 5:** The formula for matrix-vector multiplication $y = Ax$ is | + | **Problem 6:** The formula for matrix-vector multiplication $y = Ax$ is |
| <latex> | <latex> | ||
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| Write a function ''matvecmult'' that takes a matrix $A$ and a vector $x$ as inputs, computes $y = Ax$ according to that formula, and returns the vector $y$. Compare your ''matvecmult'' to Matlab's built-in matrix-vector multiplication operator ''*'' on a random $4 \times 4$ matrix and a random 4d column vector. | Write a function ''matvecmult'' that takes a matrix $A$ and a vector $x$ as inputs, computes $y = Ax$ according to that formula, and returns the vector $y$. Compare your ''matvecmult'' to Matlab's built-in matrix-vector multiplication operator ''*'' on a random $4 \times 4$ matrix and a random 4d column vector. | ||
| - | ...to be continued... | + | ---- |
| + | |||
| + | **Problem 7:** The formula for matrix-matrix multiplication $C = AB$ of an $m \times n$ matrix $A$ and an, $n \times p$ matrix $B$ is | ||
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| + | <latex> | ||
| + | C_{i,j} = \sum_{k=1}^n A_{ik} B_{k,j} \quad \text{ for } i = 1,\dots,m, \text{ and } j = 1,\dots,p, | ||
| + | </latex> | ||
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| + | The product $C = AB$ is an $m \times p$ matrix. | ||
| + | |||
| + | Write a function ''matmatmult'' that takes a matrix $A$ and a vector $x$ as inputs, computes $C = AB$ according to that formula, and returns the matrix $C$. Compare your ''matmatmult'' to Matlab's built-in matrix-vector multiplication operator ''*'' on a random $4 \times 3$ matrix $A$ and a random $3 \times 5$ matrix B. | ||
gibson/teaching/spring-2016/math445/lab5.1455561286.txt.gz · Last modified: 2016/02/15 10:34 by gibson
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