## Output from imldet1.sas

Source
0 Graphs

```NOTE: Capture of log output started.
```
```NOTE: %INCLUDE (level 1) file n:\psy6140\examples\iml\imldet1.sas is file
n:\psy6140\examples\iml\imldet1.sas.```
```265  +title 'Properties of determinants';
266  +proc iml;```
`IML Ready`
```266  +           reset print log;
267  +   /*----------------------------------------*
268  +    | IMLDET1: Properties of determinants    |
269  +    *----------------------------------------*/
270  +   A = {3 1, 2 4};```
```                A             2 rows      2 cols    (numeric)

3         1
2         4

```
`271  +   r = det(A);`
```                R             1 row       1 col     (numeric)

10

```
```272  +
273  + *-- 1. Interchange rows or cols -> -1 # det(A);
274  +   r = det(A[{2 1},]);```
```                R             1 row       1 col     (numeric)

-10

```
`275  +   r = det(A[,{2 1}]);`
```                R             1 row       1 col     (numeric)

-10

```
```276  +
277  + *-- 2. transpose -> det a unchanged;
278  +   r = det( A`);```
```                R             1 row       1 col     (numeric)

10

```
```279  +
280  + *-- 3. multiply row # k -> k # det a;
281  +   r = diag({3 1}) * A;```
```                R             2 rows      2 cols    (numeric)

9         3
2         4

```
`282  +   r = det( diag({3 1})  * A);`
```                R             1 row       1 col     (numeric)

30

```
```283  +
284  + *-- 4. multiply matrix # k -> k**2 # det(a);
285  +   r = det(3 # A);```
```                R             1 row       1 col     (numeric)

90

```
```286  +
287  + *-- 5. det (a * b) ->  det(a) #  det(b);
288  +   B={ 4 2, 3 5};```
```                B             2 rows      2 cols    (numeric)

4         2
3         5

```
`289  +   r = det(B);`
```                R             1 row       1 col     (numeric)

14

```
`290  +   r = det(A * B);`
```                R             1 row       1 col     (numeric)

140

```
`291  +   r = det(A) # det(B);`
```                R             1 row       1 col     (numeric)

140

```
```292  +
293  + *-- 6. proportional rows -> det = 0;
294  +   C={1 5, 2 6, 4 4};```
```                C             3 rows      2 cols    (numeric)

1         5
2         6
4         4

```
`295  +   C=C || C[,1];`
```                C             3 rows      3 cols    (numeric)

1         5         1
2         6         2
4         4         4

```
`296  +   r = det(C);`
```                R             1 row       1 col     (numeric)

0

```
```297  +
298  + *-- 7. Add multiple of one row to another -> det unchanged;
299  +   A[2,] = A[2,] - 2#A[1,];```
```                A             2 rows      2 cols    (numeric)

3         1
-4         2

```
`300  +   r = det(A);`
```                R             1 row       1 col     (numeric)

10

```
`301  +quit;`
`Exiting IML.`
```NOTE: The PROCEDURE IML used 0.17 seconds.

```
`302  +`
`NOTE: %INCLUDE (level 1) ending.`