Question
Download Solution PDF\(\left| {\begin{array}{*{20}{c}} {2 + i}&{2 - i}\\ {1 + i}&{i - 1} \end{array}} \right|\)का मूल्य क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
यदि \(A = \left[ {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}}\\ {{a_{21}}}&{{a_{22}}} \end{array}} \right]\) तो A का सारणिक निम्न द्वारा दिया जाता है: |A| = (a11 × a22) – (a12 – a21).
गणना:
माना कि, \({\rm{A}} = \left| {\begin{array}{*{20}{c}} {2 + i}&{2 - i}\\ {1 + i}&{i - 1} \end{array}} \right|\)
⇒ |A| = (2 + i) (i – 1) – (2 – i) (1 + i)
= 2i + i2 – 2 – i – (2 – i + 2i – i2)
= i – 1 – 2 – (2 + i + 1) (∵ i2 = -1)
= i – 3 – 2 – i – 1
= -6
∴ |A| वास्तविक संख्या है।
Last updated on May 30, 2025
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