Solving Systems of Linear Equations Using PROC IML

Suppose the system of linear equation is given below:

3x- y+2z = 8

2x-2y+3z = 2

4x+ y-4z = 9

in order to solve this equation,

| 3 -1 2 |

let A=| 2 -2 33 |

| 4 1 -4 |

be the coefficient matrix,

| 8 | | x |

C = | 2 | X = | y |

| 9 | | z |

then by using matrix language, we can write the equation as:

AX = C

and the solution of the given linear equation is:

X = C*A^-1

By using PROC IML, we can easily solve the equation. */

*--- Solving a System of Linear Equations using PROC IML;

*---SAS Program: Solve_LE.SAS;

proc iml;

reset print;

a={3 -1 2,

2 -2 3,

4 1 -4};

c={8, 2, 9};

/* Now write the solution equation, x = inv(a)*c, as an IML statement. The appropriate

statement is an assignment statement that uses a built-in function and an operator

(INV is a built-in function that takes the inverse of a square matrix, and * is the

operator for matrix multiplication).

*/

x=inv(a)*c;

quit;

SAS Output (solution is given below)

Solving System of Linear Equations

A 3 rows 3 cols (numeric)

3 -1 2

2 -2 3

4 1 -4

C 3 rows 1 col (numeric)

8

2

9

X 3 rows 1 col (numeric)

3

5

2