Low confidence that this will help, but my approach: I mentally move the right-hand matrix up, so that the space “in between” them (right of the first, below the second) is the right shape for the result. Each value of the result is the dot product of the vectors to the left and above it. (I don’t have a trick for dot products, I just know how to calculate them.)
. . . . g h i
a b c * j k l
d e f . m n o
“becomes”
. . . g h i
. . . j k l
. . . m n o
. . . -----
a b c|S T W
d e f|X Y Z
and e.g. S is (a b c) dot (g j m), Y is (d e f) dot (h k n).
Low confidence that this will help, but my approach: I mentally move the right-hand matrix up, so that the space “in between” them (right of the first, below the second) is the right shape for the result. Each value of the result is the dot product of the vectors to the left and above it. (I don’t have a trick for dot products, I just know how to calculate them.)
“becomes”
and e.g. S is (a b c) dot (g j m), Y is (d e f) dot (h k n).
By Juniper, I think this is the one. It’s simple enough that I can actually remember this, and I can solve arbitrary matrixes with this approach.
Feel free to have an internet cookie in thanks. :)
I use exactly the same approach! When you position the matrices this way, it becomes completely obvious.