Introduction to Matrices and Linear Algebra on Maple Math 2270-3 September 2, 2009 - updated September 16 - posted on our lecture page With Maple you can create combined text-math documents. Alternately, you can create math output and export it to other documents. This text field was created using the "T" menu item. To do math in a document, move your cursor to just above the place you want to do it, and use the "[>" menu item - a math field will be created as near to directly below your current cursor position as possible. If you're in a Math field and want text below it, hit the "T" menu item. 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 JSFH The newer Maple package for matrix and linear algebra is called "LinearAlgebra". Commands in LinearAlgebra tend to be concatenated capitalized words for the complete name of the procedure you wish to do. There are also shortcuts. Load the LinearAlgebra package: 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 Define a matrix: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRictRjY2LVEifkYnRjlGOy9GP0Y9RkBGQkZERkZGSEZKL0ZORkwvJStleGVjdXRhYmxlR0Y9Rjk= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Compute the reduced row echelon form: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVE2UmVkdWNlZFJvd0VjaGVsb25Gb3JtRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEiQUYnRi9GMi9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSI7RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw== Define a (column) vector: 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 Augment a matrix and a vector, or two matrices with the same number of rows: 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 Multiply two matrices (or a matrix times a column vector): 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 Matrix addition, scalar multiplication, integer powers, etc: 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 Solve a non-singular square matrix problem (non-singular means inversetransformation (and matrix) exist. We are solving Bx=b. Any one of the following commands will work! 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 Solve any solvable matrix problem. Here we are solving Ax=b: 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 JSFH