A couple of other things you could do with the tool include shuffling your channels and doing color correction. For instance, if you wanted to see only the grayscale red channel, you could enter 1,0,0,0 into all three lines. Each channel would then be replaced with the red channel.

Color correction: Say you want the image to be slightly yellower. In additive color theory, yellow is complementary to blue, so that means you need to reduce the blue information in the matrix. Give the blue line 0, 0, .9, 0 That will reduce the blue by 10%, which effectively increases the yellow.

A color wash, like the sepia preset, can be achieved by starting with the grayscale preset, then nudging the numbers in the direction you want to go. Notice that sepia is pretty close to the numbers for gray. The blue has been pushed down, and both red and green raised, red a bit more than green. It will likely take a lot of experimentation to hit the numbers you want, but starting with a good understanding of additive color theory will help.

Incidentally, this matrix is frequently used to construct Photoshop filters, as is the Spatial Matrix Process.