- To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. Here, the first matrix is 2x3 and the second is 3x2, so multiplication is valid, resulting in a 2x2 matrix.
- The element in row i, column j of the result is found by multiplying corresponding elements of row i from the first matrix and column j from the second matrix, then summing those products.
- For the element at row 1, column 1: (2)(2) + (0)(4) + (1)(8) = 4 + 0 + 8 = 12.
- For the element at row 1, column 2: (2)(1) + (0)(-3) + (1)(10) = 2 + 0 + 10 = 12.
- For the element at row 2, column 1: (2)(2) + (1)(4) + (2)(8) = 4 + 4 + 16 = 24.
- For the element at row 2, column 2: (2)(1) + (1)(-3) + (2)(10) = 2 - 3 + 20 = 19.
- The resulting matrix is [[12, 12], [24, 19]].
Parent Tip: Review the logic above to help your child master the concept of multiplying matrices worksheet.
