Math 206  

Fall 2009 

 

> Typesetting:-mrow(Typesetting:-mi(
 

> with(linalg); -1
 

 

Multiplying Matrices and Finding Inverses in Maple 

 

These examples are taken from your 2.2:  The Inverse of a Matrix lecture notes.  These examples illustrate how to multiply matrices and find inverses in Maple. 

 

Example 1. 

> `:=`(A, matrix(2, 2, [4, 9, 3, 7])); 1
 

array( 1 .. 2, 1 .. 2, [( 2, 1 ) = 3, ( 1, 1 ) = 4, ( 2, 2 ) = 7, ( 1, 2 ) = 9 ] ) (1)
 

> `:=`(B, matrix(2, 2, [7, -9, -3, 4])); 1
 

array( 1 .. 2, 1 .. 2, [( 2, 1 ) = -3, ( 1, 1 ) = 7, ( 2, 2 ) = 4, ( 1, 2 ) = -9 ] ) (2)
 

> multiply(A, B); 1
 

array( 1 .. 2, 1 .. 2, [( 2, 1 ) = 0, ( 1, 1 ) = 1, ( 2, 2 ) = 1, ( 1, 2 ) = 0 ] ) (3)
 

> multiply(B, A); 1
 

array( 1 .. 2, 1 .. 2, [( 2, 1 ) = 0, ( 1, 1 ) = 1, ( 2, 2 ) = 1, ( 1, 2 ) = 0 ] ) (4)
 

 

Example 4. 

 

> `:=`(A, matrix(2, 2, [4, 9, 3, 7])); 1
 

array( 1 .. 2, 1 .. 2, [( 2, 1 ) = 3, ( 1, 1 ) = 4, ( 2, 2 ) = 7, ( 1, 2 ) = 9 ] ) (5)
 

> `:=`(b, matrix(2, 1, [6, 18])); 1
 

array( 1 .. 2, 1 .. 1, [( 2, 1 ) = 18, ( 1, 1 ) = 6 ] ) (6)
 

> `:=`(X, multiply(inverse(A), b))
 

array( 1 .. 2, 1 .. 1, [( 2, 1 ) = 54, ( 1, 1 ) = -120 ] ) (7)
 

Example 5. 

> `:=`(A, matrix(3, 3, [1, 3, 4, -2, -5, -3, 1, 4, 9])); 1
 

array( 1 .. 3, 1 .. 3, [( 3, 2 ) = 4, ( 1, 3 ) = 4, ( 2, 1 ) = -2, ( 1, 1 ) = 1, ( 3, 1 ) = 1, ( 2, 2 ) = -5, ( 1, 2 ) = 3, ( 2, 3 ) = -3, ( 3, 3 ) = 9 ] ) (8)
 

> Typesetting:-mrow(Typesetting:-mi(
 

Error, (in linalg:-inverse) singular matrix
 

Example 7. 

> `:=`(B, matrix(3, 4, [3, -1, 2, 6, 7, 4, 1, 5, 5, 2, 4, 1])); 1
 

array( 1 .. 3, 1 .. 4, [( 3, 2 ) = 2, ( 1, 3 ) = 2, ( 2, 4 ) = 5, ( 2, 1 ) = 7, ( 1, 1 ) = 3, ( 3, 1 ) = 5, ( 3, 4 ) = 1, ( 2, 2 ) = 4, ( 1, 4 ) = 6, ( 1, 2 ) = -1, ( 2, 3 ) = 1, ( 3, 3 ) = 4 ] ) (9)
 

> `:=`(A, matrix(3, 3, [4, 3, 2, 5, 6, 3, 3, 5, 2])); 1
 

array( 1 .. 3, 1 .. 3, [( 3, 2 ) = 5, ( 1, 3 ) = 2, ( 2, 1 ) = 5, ( 1, 1 ) = 4, ( 3, 1 ) = 3, ( 2, 2 ) = 6, ( 1, 2 ) = 3, ( 2, 3 ) = 3, ( 3, 3 ) = 2 ] ) (10)
 

> inverse(A)
 

array( 1 .. 3, 1 .. 3, [( 3, 2 ) = 11, ( 1, 3 ) = 3, ( 2, 1 ) = 1, ( 1, 1 ) = 3, ( 3, 1 ) = -7, ( 2, 2 ) = -2, ( 1, 2 ) = -4, ( 2, 3 ) = 2, ( 3, 3 ) = -9 ] ) (11)
 

> `:=`(X, multiply(inverse(A), B))
 

array( 1 .. 3, 1 .. 4, [( 3, 2 ) = 33, ( 1, 3 ) = 14, ( 2, 4 ) = -2, ( 2, 1 ) = -1, ( 1, 1 ) = -4, ( 3, 1 ) = 11, ( 3, 4 ) = 4, ( 2, 2 ) = -5, ( 1, 4 ) = 1, ( 1, 2 ) = -13, ( 2, 3 ) = 8, ( 3, 3 ) = -3... (12)
 

> multiply(A, X)
 

array( 1 .. 3, 1 .. 4, [( 3, 2 ) = 2, ( 1, 3 ) = 2, ( 2, 4 ) = 5, ( 2, 1 ) = 7, ( 1, 1 ) = 3, ( 3, 1 ) = 5, ( 3, 4 ) = 1, ( 2, 2 ) = 4, ( 1, 4 ) = 6, ( 1, 2 ) = -1, ( 2, 3 ) = 1, ( 3, 3 ) = 4 ] ) (13)