Question
Download Solution PDFयदि \(\rm A=\begin{bmatrix} 1& 3\\ 5& 2\end{bmatrix}\) और \(\rm B=\begin{bmatrix} 3&2\\ 1& 3\end{bmatrix}\) तो |AB| = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
आव्यूहों के गुणनफल का सारणिक आव्यूहों के सारणिकों के गुणनफल के बराबर है।
यानी |AB| = |A| |B|
गणना:
दिया हुआ है कि \(\rm A=\begin{bmatrix} 1& 3\\ 5& 2\end{bmatrix}\) \(\rm B=\begin{bmatrix} 3&2\\ 1& 3\end{bmatrix}\)
अब, |AB| = |A| |B| = (2 - 15)(9 - 2) = -91
Additional Information :
आव्यूह गुणनफल AB \(\rm \begin{bmatrix} 1& 3\\ 5& 2\end{bmatrix}\begin{bmatrix} 3& 2\\ 1& 3\end{bmatrix}\) = \(\begin{bmatrix} 3+3& 2+9\\ 15+2& 10+6\end{bmatrix}\) = \(\begin{bmatrix} 6& 11\\ 17& 16\end{bmatrix}\) हो जाएगा।
और |AB| = 96 - 187 = -91
Last updated on Jun 20, 2025
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