\(\left|\begin{array}{ccc} 2 x-4 & 4 & 0 \\ 2 & x-1 & 1 \\ 2 & 2 & 0 \end{array}\right|=0\) అయితే, x = ?

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  1. 4
  2. -4 
  3. -5
  4. 5

Answer (Detailed Solution Below)

Option 1 : 4
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ఇవ్వబడింది:

\(\left|\begin{array}{ccc} 2 x-4 & 4 & 0 \\ 2 & x-1 & 1 \\ 2 & 2 & 0 \end{array}\right|=0\)

భావన:

నిర్ణాయక విస్తరణ భావనను ఉపయోగించండి.

లెక్కింపు:

\(\left|\begin{array}{ccc} 2 x-4 & 4 & 0 \\ 2 & x-1 & 1 \\ 2 & 2 & 0 \end{array}\right|=0\)

మూడవ నిలువు వరుసకు సంబంధించి విస్తరించండి, అప్పుడు మనకు లభిస్తుంది

\(\rm 0-1((2x-4)\times(2)-2\times4)+0=0\)

⇒ 4x - 8 - 8 = 0

⇒ 4x = 16

⇒ x = 4

కాబట్టి ఎంపిక (1) సరైనది.

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