যদি C=AB হয়, যেখানে  A=|(1,2,3),(3,2,1),(1,1,2)| ও  B=|(1,1,2),(1,2,3),(3,2,1)| হয় তবে C এর আকার হলো?

🤔 প্রশ্ন: যদি C=AB হয়, যেখানে \(A=\begin{bmatrix} 1 & 2 & 3 \\ 3 & 2 & 1 \\ 1 & 1 & 2 \end{bmatrix}\) ও \(B=\begin{bmatrix} 1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 2 & 1 \end{bmatrix}\) হয় তবে C এর আকার হলো?

💡 উত্তর: \(C = AB\) হলে, \(C\) এর উপাদানগুলো নির্ণয় করা যাক:

\(C_{11} = (1 \times 1) + (2 \times 1) + (3 \times 3) = 1 + 2 + 9 = 12\)
\(C_{12} = (1 \times 1) + (2 \times 2) + (3 \times 2) = 1 + 4 + 6 = 11\)
\(C_{13} = (1 \times 2) + (2 \times 3) + (3 \times 1) = 2 + 6 + 3 = 11\)
\(C_{21} = (3 \times 1) + (2 \times 1) + (1 \times 3) = 3 + 2 + 3 = 8\)
\(C_{22} = (3 \times 1) + (2 \times 2) + (1 \times 2) = 3 + 4 + 2 = 9\)
\(C_{23} = (3 \times 2) + (2 \times 3) + (1 \times 1) = 6 + 6 + 1 = 13\)
\(C_{31} = (1 \times 1) + (1 \times 1) + (2 \times 3) = 1 + 1 + 6 = 8\)
\(C_{32} = (1 \times 1) + (1 \times 2) + (2 \times 2) = 1 + 2 + 4 = 7\)
\(C_{33} = (1 \times 2) + (1 \times 3) + (2 \times 1) = 2 + 3 + 2 = 7\)

অতএব, \(C = \begin{bmatrix} 12 & 11 & 11 \\ 8 & 9 & 13 \\ 8 & 7 & 7 \end{bmatrix}\) 🎉