PRETTY_MAT_1_ID = printSimpleMatrix(MAT_1)
PRETTY_MAT_2_ID = printSimpleMatrix(MAT_2)
What is PRETTY_MAT_1_ID + PRETTY_MAT_2_ID?
Because PRETTY_MAT_1_ID has dimensions (DIM_1 + "\\times" + DIM_2) and PRETTY_MAT_2_ID has dimensions (DIM_3 + "\\times" + DIM_4), the answer matrix will have dimensions (DIM_1 + "\\times" + DIM_4).
PRETTY_MAT_1_ID + PRETTY_MAT_2_ID
=
printColoredDimMatrix(MAT_1, ROW_COLORS, true)
printColoredDimMatrix(MAT_2, COL_COLORS, false)
=
printSimpleMatrix(maskMatrix(FINAL_HINT_MAT, []))
To find the element at any row i, column j of the answer matrix, multiply the elements in row i of the first matrix, PRETTY_MAT_1_ID, with the corresponding elements in column j of the second matrix, PRETTY_MAT_2_ID, and add the products together.
So, to find the element at row 1, column 1 of the answer matrix, multiply the first element in colorMarkup("\\text{" + ROW + " }1", ROW_COLORS[0]) of PRETTY_MAT_1_ID with the first element in colorMarkup("\\text{" + COLUMN + " }1", COL_COLORS[0]) of PRETTY_MAT_2_ID, then multiply the second element in colorMarkup("\\text{" + ROW + " }1", ROW_COLORS[0]) of PRETTY_MAT_1_ID with the second element in colorMarkup("\\text{" + COLUMN + " }1", COL_COLORS[0]) of PRETTY_MAT_2_ID, and so on. Add the products together.
printSimpleMatrix(
maskMatrix(FINAL_HINT_MAT, [[1, 1]])
)
Likewise, to find the element at row 2, column 1 of the answer matrix, multiply the elements in colorMarkup("\\text{" + ROW + " }2", ROW_COLORS[1]) of PRETTY_MAT_1_ID with the corresponding elements in colorMarkup("\\text{" + COLUMN + " }1", COL_COLORS[0]) of PRETTY_MAT_2_ID and add the products together.
printSimpleMatrix(
maskMatrix(FINAL_HINT_MAT, [[1, 1], [2, 1]])
)
Fill out the rest:
printSimpleMatrix(FINAL_HINT_MAT)
After simplifying, we end up with:
printSimpleMatrix(SOLN_MAT)