How do you multiply this set of matrices?
[5 4 8] \/ {-8 6}
[3 -4 -2] /\ { 0 -2}
The first matrix is a 2x3 and the second one is a 2x2.
You can only multiply an n×m matrix on the left by an
m×p matrix on the right.
The inner two dimensions must match or you can't
multiply them:
Examples:
A 5×8 matrix on the left CAN be multiplied by an 8×4
matrix on the right because the two inner dimensions
are both the same, namely 8.
An 8×4 matrix on the left CANNOT be multiplied by an 5×8
matrix on the right because the two inner dimensions
are not the same, one being 4 and the other 5.
A 5×8 matrix on the left CAN be multiplied by an 8×4
matrix on the right because the two inner dimensions
are both the same, namely 8.
An 6×4 matrix on the left CAN be multiplied by an 4×1
matrix on the right because the two inner dimensions
are both the same, namely 4.
In your case, you CANNOT multiply them because you
have a 2×3 on the left and a 2×2 matrix on the
right, and the inner dimensions, 3 and 2, do not match.
Now if you had those two matrices reversed, you
COULD multiply them, for then you'd have a 2×2 matrix
on the left and a 2×3 on the right and the inner
dimensions would both equal 2.
[-8 6] \/ {5 4 8}
[ 0 -2] /\ {3 -4 -2}
then the answer would have been this 2×3 matrix
[-22 -56 -76]
[ -6 8 4]
If you need to learn how to multiply two matrices
when they CAN be multiplied, repost asking how.
Edwin
