Question
Download Solution PDFk के कितने मानों के लिए आव्यूह \(\left[ {\begin{array}{*{20}{c}} 0&{\rm{k}}&4\\ { - {\rm{k}}}&0&{ - 5}\\ { - {\rm{k}}}&{\rm{k}}&{ - 1} \end{array}} \right]\) अव्युत्क्रमणीय है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि |A| = 0 है, तो आव्यूह अव्युत्क्रमणीय है।
गणना:
दी गयी आव्यूह \(\left[ {\begin{array}{*{20}{c}} 0&{\rm{k}}&4\\ { - {\rm{k}}}&0&{ - 5}\\ { - {\rm{k}}}&{\rm{k}}&{ - 1} \end{array}} \right]\)अव्युत्क्रमणीय है।
हम जानते हैं कि यदि |A| = 0 है, तो आव्यूह अव्युत्क्रमणीय है।
⇒\(\rm\begin{vmatrix} 0 &k &4 \\ -k &0 &-5 \\ -k &k &-1 \end{vmatrix} = 0\)
⇒ 0 - k (k - 5k) + 4 (- k2) = 0
⇒ 4k2 - 4k2 = 0
इसलिए, हम k का कोई भी मान ले सकते हैं, जो इसे अव्युत्क्रमणीय आव्यूह बनाता है।
अतः k का कुल मान अनंत है।
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