How do you multiply #((1, -3, 2), (2, 1, -3), (4, -3, -1))# and #((1, 4, 1, 0), (2, 1, 1, 1), (1, -2, 1, 2))#?

1 Answer
May 30, 2016

#((-3,-3,0,1),(1,15,0,-5),(-1,11,2,-1))#

Explanation:

Matrices could be multiplied only if first one has as many columns as the second one has rows. In that case it's true - first has 3 columns and second has 3 rows, so we can multiply.
The result will have as many rows as first matrix and as many columns as second matrix.
Everything will be clear from following instruction:

  • Lift the second matrix to make room for result.
  • To obtain any element take a row directly to the left of it and a column directly above it (for the first element it is #((1, -3, 2))# and #((1), (2), (1))#)
  • multiply them pairwise and take sum: #1*1+(-3)*2+2*1=1-6+2=-3#
  • the number you get is this element of resulting matrix

Here is the whole thing:

#color(white)(------0)((1,4,1,0),(2,1,1,1),(1,-2,1,2))#
#((1,-3,2),(2,1,-3),(4,-3,1))((-3,-3,0,1),(1,15,0,-5),(-1,11,2,-1))#

For other multiplying examples:
How do I do multiplication of matrices?
use wolfram alpha
just google it
use excel (if possible)