Question
Download Solution PDFA = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) और B = \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\) है, तो (AB)T का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
आव्यूह का पक्षांतर:
साधारण आव्यूह के पंक्तियों और स्तंभों को एक-दूसरे से परिवर्तित करके प्राप्त नए आव्यूह को आव्यूह का पक्षांतर कहा जाता है।
इसे A′ या AT द्वारा दर्शाया गया है।
गणना:
दिया गया है A = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) और B = \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\)
AB = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) × \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\)
AB = \(\begin{bmatrix} 1-3+0 \\ 3+6-5 \end{bmatrix}\)
AB = \(\begin{bmatrix} -2 \\ 4 \end{bmatrix}\)
∴ (AB)T = \(\begin{bmatrix} -2 & 4 \end{bmatrix}\)
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