Question - Matrix Multiplication Result
Solution:
The image shows two matrices that need to be multiplied. Let's call the first matrix A and the second matrix B:Matrix A =[3 2 5][2 3 1]Matrix B =[4 5 -5][5 -1 6][4 5 -5]To multiply two matrices, we can use the following formula for the elements of the resulting matrix:Given matrices A (of size m by n) and B (of size n by p), their product C (of size m by p) will have elements:\[ c_{ij} = \sum_{k=1}^{n} a_{ik} \cdot b_{kj} \]So for matrices A (2x3) and B (3x3), we can find the product C (2x3) by multiplying each row of A with each column of B.Let's perform the multiplication:\[ c_{11} = (3 \times 4) + (2 \times 5) + (5 \times 4) = 12 + 10 + 20 = 42 \]\[ c_{12} = (3 \times 5) + (2 \times -1) + (5 \times 5) = 15 - 2 + 25 = 38 \]\[ c_{13} = (3 \times -5) + (2 \times 6) + (5 \times -5) = -15 + 12 - 25 = -28 \]\[ c_{21} = (2 \times 4) + (3 \times 5) + (1 \times 4) = 8 + 15 + 4 = 27 \]\[ c_{22} = (2 \times 5) + (3 \times -1) + (1 \times 5) = 10 - 3 + 5 = 12 \]\[ c_{23} = (2 \times -5) + (3 \times 6) + (1 \times -5) = -10 + 18 - 5 = 3 \]So the product C of the matrices A and B is:Matrix C =[42 38 -28][27 12 3]
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