Maple Project 4 Demonstration Recall from Maple Project 2 that we can define matrices in Maple by first including the LinearAlgebra package LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRLkxpbmVhckFsZ2VicmFGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= then enter a matrix by hand, using the command Matrix 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKCcqZWEi

This is an example of a 2x2 matrix. The LinearAlgebra package has commands Eigenvalues and Eigenvectors, which will compute the eigenvalues and eigenvectors of M. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEsRWlnZW52YWx1ZXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJNRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjtGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYn

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoJ0g1Pg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEtRWlnZW52ZWN0b3JzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEiTUYnRi9GMi9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSI7RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiQtJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIihXYisjLUknTWF0cml4R0YmNiMvRi4iKEc/LCM=

Here, the Eigenvectors command returns a list of data, where the first result is a vector with entries equal to the eigenvalues, and the second result is a matrix with ith column equal to an eigenvector for the ith eigenvalue. These are somewhat messy numbers. To convert them to decimals, you may enclose the Eigenvalues/Eigenvectors command in evalf: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSxFaWdlbnZhbHVlc0YnRi9GMi1GNjYkLUYjNiMtRiw2JVEiTUYnRi9GMi9GM1Enbm9ybWFsRidGRC1JI21vR0YkNi1RIjtGJ0ZELyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkwvJSpzeW1tZXRyaWNHRkwvJShsYXJnZW9wR0ZMLyUubW92YWJsZWxpbWl0c0dGTC8lJ2FjY2VudEdGTC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYn

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print(); # input placeholder

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoW1ksIw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUS1FaWdlbnZlY3RvcnNGJ0YvRjItRjY2JC1GIzYjLUYsNiVRIk1GJ0YvRjIvRjNRJ25vcm1hbEYnRkQtSSNtb0dGJDYtUSI7RidGRC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZMLyUqc3ltbWV0cmljR0ZMLyUobGFyZ2VvcEdGTC8lLm1vdmFibGVsaW1pdHNHRkwvJSdhY2NlbnRHRkwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiQtJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIigpWz4/LUknTWF0cml4R0YmNiMvRi4iKCtjLSM=

The next LinearAlgebra command you will need to recall for this project is MatrixInverse. To compute the inverse of M, take LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEuTWF0cml4SW52ZXJzZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRIk1GJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKEsuLiM=

To create a plot of a polar function on a polar graph, include the package "plots" and use the command "polarplot". For example, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJnBsb3RzRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQ= 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqJiIiIyIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiIiJEYlSSJ3R0YrRiVGJUYlRiU=

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These should be basically all the commands you need for this assignment (!), up to defining the appropriate functions, differential equations, constants, matrices, etc, regular (non-polar) plotting, and matrix multiplication. The rest of the work for the project should be done by hand. You should look at this project as two very good examples of how we can work together with Maple to process data and solve application-type problems for systems of differential equations. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= To create a plot on a polar graph, include te package "plots", and use the command "polarplot" Basically everything else in this project should be done by hand. Of coruse, you will need to define functions, differential equations, constants, matrices, etc. in Maple as appropriate. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= TTdSMApJNFJUQUJMRV9TQVZFLzE1NDU4OTZYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMlIiMiIyIiIiIiJCIiIyIiJTYiTTdSMApJNFJUQUJMRV9TQVZFLzE5MTAyOTZYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMsJiMiIiYiIiMiIiIqJCIjTCNGK0YqRi4sJkYoRitGLCMhIiJGKjYiTTdSMApJNFJUQUJMRV9TQVZFLzIwMDU1NDRYKiUqYWxnZWJyYWljRzYiNiJbZ2whIyUhISEiIyIjLCYjIiImIiIjIiIiKiQiI0wjRitGKkYuLCZGKEYrRiwjISIiRio2Ig==TTdSMApJNFJUQUJMRV9TQVZFLzIwMTIwMjhYLCUqYWxnZWJyYWljRzYiNiJbZ2whIiUhISEjJSIjIiMsJCokLCYjIiIkIiIjIiIiKiQiI0wjRi1GLEYwISIiRixGLSwkKiQsJkYqRi1GLiNGMUYsRjFGLEYtNiI=TTdSMApJNFJUQUJMRV9TQVZFLzIwMTQ2NDhYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMkIitDOEdzYCEiKiQhKkM4R3MkRik2Ig==TTdSMApJNFJUQUJMRV9TQVZFLzIwMTk0ODhYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMkIitDOEdzYCEiKiQhKkM4R3MkRik2Ig==TTdSMApJNFJUQUJMRV9TQVZFLzIwMjU2MDBYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMlIiMiIyQiK3c1RnVYISM1JCIiIiIiISQhKzJyVWQ5ISIqRio2Ig==TTdSMApJNFJUQUJMRV9TQVZFLzIwMzAzMzJYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMlIiMiIyEiIyMiIiQiIiMiIiIjISIiRio2Ig==