Answer:
 |
0.5 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.5 |
 |
|
2 4 6 0 -12 -8 4 0 4 |
|
= | (0.5)I | |
2 4 6 0 -12 -8 4 0 4 |
|
= |
| 0.5 | |
2 4 6 0 -12 -8 4 0 4 |
|
= | |
1 2 3 0 -6 -4 2 0 2 |
|
|
0.5 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.5 |
|
|
2 4 6 0 -12 -8 4 0 4 |
|
= | (0.5)I | |
2 4 6 0 -12 -8 4 0 4 |
|
= |
| 0.5 | |
2 4 6 0 -12 -8 4 0 4 |
|
= | |
1 2 3 0 -6 -4 2 0 2 |
|
The diagonal matrix (aI) is sometimes useful in computer graphics. Say for example that what you want to compute is:
a Ax
where a is a scalar and x is a column matrix. Sometimes it is convenient to think of this as:
(aI)Ax
Now every operation is a matrix multiplication. This is an advantage since matrix multiplication can be done by graphics hardware.
What is (2I)(0.5I)?