Practice question · Put in order
Order the steps of computing the entry in row 2, column 3 of the product AB.
- Multiply matching entries of that row and column and add the results
- Take column 3 of B
- Check that the number of columns of A equals the number of rows of B
- Write the total into position (2, 3) of AB
- Take row 2 of A
Hints
- Confirm the product exists at all before computing anything.
- The row index selects from A and the column index selects from B.
Show the answer
- Check that the number of columns of A equals the number of rows of B
- Take row 2 of A
- Take column 3 of B
- Multiply matching entries of that row and column and add the results
- Write the total into position (2, 3) of AB
Why
Check the inner dimensions, pick row i from A and column j from B, dot them, and place the number. The index pattern is fixed: the ROW index always refers to the left matrix and the COLUMN index to the right one, which is why AB and BA build entries from entirely different data.
Practise Matrices and Matrix Operations
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