Worksheet #1

Doing some Linear Algebra in Maple

A little basic maple.

To evaluate an expression, enter it at the prompt. End a statement with a semicolon.

2+3;

IiIm

5+9;

IiM5

% refers to the last answer, and %% to the next to last answer.

% + %%;

IiM+

It's best not to overuse these! To assign to a variable, use := (colon -equal);

a := 7;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJhR0YoIiIoNyNGLg==

IiIo

3+a;

IiM1

a := (x+y)^3;

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a := expand(a);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJhR0YoLCoqJClJInhHRigiIiQiIiJGMyooRjJGMylGMSIiI0YzSSJ5R0YoRjNGMyooRjJGM0YxRjMpRjdGNkYzRjMqJClGN0YyRjNGMzcjRi4=

subs(x=3, y=2, a);

IiREIg==

x := 3; y:=2;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ4R0YoIiIkNyNGLg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ5R0YoIiIjNyNGLg==

IiREIg==

To make x, y, and a symbols again, do this.

a := 'a'; x := 'x'; y:= 'y';

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LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ4R0YoRi03I0Yt

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ5R0YoRi03I0Yt

SSJhRzYi

Using a colon instead of a semicolon supresses the output of the statement.

a := 10!:

IigrKUdP

Basic linear algebra.

First, load the student linear algebra package

with(LinearAlgebra): with(Student[LinearAlgebra]):

The starting page for help on this package is Student, LinearAlgebra

?Student, LinearAlgebra

There are lots of ways to specify a matrix or vector. See the help pages for Matrix (with a capital M) and Vector. I'll show the shortcuts.

To enter a vector, use angle brackets <>. Use commas to seperate rows and vertical bars (|) to seperate columns.

Here's a row vector

v1 := <1|7|-5>;

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Here's a column vector

w1 := <0, 2, 1>;

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

To build a matrix, put together column vectors, or put together row vectors.

Here is a matrix specified by rows. The whitespace is ignored

A := <<1|2|3>, <4|0|1>, <3|1|2>>;

Here's a matrix specified by columns

B :=< <1,2,1> | <3, -1,2> | <4, 0, 5>>;

Adding w1 to the right of A

C := <A|w1>;

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Adding v1 to the top of A

E := <v1,A>;

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Joining vectors into a matrix

u1 := <1,2,1>; u2 := <-1, 1, 2>; u3 := <7,-1,2>;

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LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN1M0dGKC1JJ1JUQUJMRUdGKDYlIihvYGooLUknTUFUUklYR0YoNiM3JTcjIiIoNyMhIiI3IyIiIyZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GPDYjL0kkJWlkR0YoRjE=

F :=<u1|u2|u3>;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKSZBc3NpZ247RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNigtSSdtdGFibGVHRiQ2Ny1JJG10ckdGJDYoLUkkbXRkR0YkNigtSSNtbkdGJDYkUSIxRidGOS8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGW28vJStncm91cGFsaWduR0Zbby8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0Ziby1GWTYoLUZmbjYkUSsmdW1pbnVzMDsxRidGOUZpbkZcb0Zeb0Zgb0Zjby1GWTYoLUZmbjYkUSI3RidGOUZpbkZcb0Zeb0Zgb0Zjb0ZpbkZcb0Zeby1GVjYoLUZZNigtRmZuNiRRIjJGJ0Y5RmluRlxvRl5vRmBvRmNvRlhGZW9GaW5GXG9GXm8tRlY2KEZYRmFwRmFwRmluRlxvRl5vLyUmYWxpZ25HUSVheGlzRicvRmpuUSliYXNlbGluZUYnL0Zdb1EnY2VudGVyRicvRl9vUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGMS8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmVxLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmByLyUmZnJhbWVHRmByLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGPS8lLWVxdWFsY29sdW1uc0dGPS8lLWRpc3BsYXlzdHlsZUdGPS8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZdckY5L0krbXNlbWFudGljc0dGJFEnTWF0cml4RicvJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0YnRmNz

Generate a random matrix.

G := RandomMatrix(3, 3);

Generate a BIG random Matrix

G := RandomMatrix(20,20);

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

That was to big to print out. To look at it, double click on the square brackets above to get a matrix browser.

Matrix addition and subtraction work as expected.

A+B;

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

A-B;

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

To multiply a scalar times a matrix, use * or /.

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

10*A;

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

A/3;

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

To multiply matrices, use . (period).

A, B;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYoLUknbXRhYmxlR0YkNjctSSRtdHJHRiQ2KC1JJG10ZEdGJDYoLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGQC8lK2dyb3VwYWxpZ25HRkAvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGRy1GNTYoLUY4NiRRIjJGJ0Y7Rj5GQUZDRkVGSC1GNTYoLUY4NiRRIjNGJ0Y7Rj5GQUZDRkVGSEY+RkFGQy1GMjYoLUY1NigtRjg2JFEiNEYnRjtGPkZBRkNGRUZILUY1NigtRjg2JFEiMEYnRjtGPkZBRkNGRUZIRjRGPkZBRkMtRjI2KEZPRjRGSkY+RkFGQy8lJmFsaWduR1ElYXhpc0YnL0Y/USliYXNlbGluZUYnL0ZCUSdjZW50ZXJGJy9GRFEnfGZybGVmdHxockYnLyUvYWxpZ25tZW50c2NvcGVHUSV0cnVlRicvJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0Zqby8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0ZlcC8lJmZyYW1lR0ZlcC8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHUSZmYWxzZUYnLyUtZXF1YWxjb2x1bW5zR0ZfcS8lLWRpc3BsYXlzdHlsZUdGX3EvJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dGYnBGOy9JK21zZW1hbnRpY3NHRiRRJ01hdHJpeEYnLyUlb3BlbkdRJyZsc3FiO0YnLyUmY2xvc2VHUScmcnNxYjtGJ0ZpcS1JI21vR0YkNi1RKCZjb21tYTtGJ0Y7LyUmZmVuY2VHRl9xLyUqc2VwYXJhdG9yR0Znby8lKXN0cmV0Y2h5R0ZfcS8lKnN5bW1ldHJpY0dGX3EvJShsYXJnZW9wR0ZfcS8lLm1vdmFibGVsaW1pdHNHRl9xLyUnYWNjZW50R0ZfcS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNigtRi82Ny1GMjYoRjRGT0ZWRj5GQUZDLUYyNihGSi1GNTYoLUY4NiRRKyZ1bWludXMwOzFGJ0Y7Rj5GQUZDRkVGSEZlbkY+RkFGQy1GMjYoRjRGSi1GNTYoLUY4NiRRIjVGJ0Y7Rj5GQUZDRkVGSEY+RkFGQ0Zcb0Zfb0Zhb0Zjb0Zlb0Zob0ZbcEZdcEZgcEZjcEZmcEZocEZqcEZdcUZgcUZicUZkcUZncUY7RmlxRlxyRl9yRmlx

A.B;

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

Exponents work as expected

A.A;

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

A^2;

A^(-1);

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

A. A^(-1);

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

There are two ways to do transpose.

Transpose(A);

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

A^%T;

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

The percent sign is a little ugly, I agree.

To get a matrix element, use square brackets

A[2,3];

IiIi

A[2,3]:=17;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiQUdGKDYkIiIjIiIkIiM8NyNGMg==

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

To extract rows or columns, use the commands Row and Column

For example, extract the column vectors of A

Column(A, 1..3);

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

Extract Rows 1 and 3 of A

Row(A, [1,3]);

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

More generally, there is SubMatrix.

For example, extract the 2 x 2 matrix in the upper left hand corner of A.

SubMatrix(A, 1..2, 1..2);

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

To get the RREF, use the command ReducedRowEchelonForm.

ReducedRowEchelonForm(A);

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

B := Matrix([[2, -3, -8, -8, 20], [1, -1, -3, -4, 11], [6, -3, -12, -10, 30], [-7, 0, 7, 13, -46], [-1, 1, 3, 0, 1]]);

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

ReducedRowEchelonForm(B);

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

Problem. In each case, use Reduced Row Echelon Form to determine if A is invertible and, if so, to find the inverse of A. Verify your

answer by multiplying it with A.

Part A.

A := Matrix([[2, 1, 1, 0, 0], [-30, 21, -6, -15, 1], [10, -7, 2, 5, 0], [-86, 60, -17, -45, 3], [-88, 63, -17, -45, 3]]);

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Part B.

A := Matrix([[-5, -65, 55, 26], [0, 10, -10, -3], [10, 97, -77, -44], [4, 52, -44, -21]]);

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Problem. In each part, use InverseTutor to do row operations one at a time to determine if A is invertible and, if so, find the inverse.

Check your answer by multiplication.

Part A.

A := Matrix([[1, 1, 5], [-1, 1, 5], [2, -1, -10]]);

InverseTutor(A);

Part B.

A := Matrix([[3, 4, 10], [2, 4, 12], [2, 2, 4]]);

InverseTutor(A);