Prove the following distributive property: (A+B)C = AC + BC. Let A = [aij] be an mxn matrix, B = [bij] be an mxn matrix, and C = [cjk] be an nxp matrix.
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Step 1
The element in the i-th row and j-th column of (A+B)C can be represented as: $((A+B)C)_{ij} = \sum_{k=1}^n (A+B)_{ik} \cdot C_{kj}$ Since $(A+B)_{ik} = A_{ik} + B_{ik}$, we can rewrite the above expression as: $((A+B)C)_{ij} = \sum_{k=1}^n (A_{ik} + B_{ik}) Show more…
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