Mathematics

Matrix multiplication only works when dimensions align: the number of columns in one matrix must equal the number of rows in the next. Here, you know $P$ is $4 \times 6$, the product $PQR$ is $4 \times 3$, and $R$ has 30 elements. Work backwards from $R$'s dimensions—if it has 30 elements and you can figure out one dimension from the multiplication chain, the other follows. Then use the constraint that $PQ$ must produce a matrix whose columns match $R$'s rows.

Matrix multiplication only works when dimensions align: the number of columns in one matrix must equal the number of rows in the next. Here, you know $P$ is $4 \times 6$, the product $PQR$ is $4 \times 3$, and $R$ has 30 elements. Work backwards from $R$'s dimensions—if it has 30 elements and you can figure out one dimension from the multiplication chain, the other follows. Then use the constraint that $PQ$ must produce a matrix whose columns match $R$'s rows.