Changing a tiny image shows row and column shadows as exact sums. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Grid one gives row sums three and seven
Pixels 1, 2, 3, and 4 give row sums 3 and 7.
1+2=33+4=7
Swapping columns changes column sums
Pixels 2, 1, 4, and 3 keep row sums 3 and 7 but columns become 6 and 4.
2+4=61+3=4
Larger cells raise every projection ledger
Pixels 2, 3, 4, and 5 give rows 5 and 9, columns 6 and 8.