Practice question · Put in order
Order the steps to compute entry (2,1) of AB, where A has rows (1,2),(3,4) and B has rows (5,6),(7,8).
- Take column 1 of B: (5, 7)
- Get 15 + 28 = 43
- Take row 2 of A: (3, 4)
- Form the dot product 3*5 + 4*7
Hints
- Entry (i, j) pairs row i of the left matrix with column j of the right.
- Multiply matching components and sum.
Show the answer
- Take row 2 of A: (3, 4)
- Take column 1 of B: (5, 7)
- Form the dot product 3*5 + 4*7
- Get 15 + 28 = 43
Why
Entry (2,1) uses A's row 2 and B's column 1: (3,4) dot (5,7) = 15 + 28 = 43. The row index picks the left row, the column index picks the right column.
Practise Matrices and Matrix Operations
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