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కింది ప్రకటనలలో ఏది నిజం:

1. ప్రతి గుర్తింపు మాత్రిక, I యొక్క ఆర్డర్ n అనేది ఎగువ త్రిభుజాకార మాత్రిక.

2. ప్రతి గుర్తింపు మాత్రిక, I యొక్క ఆర్డర్ n అనేది తక్కువ త్రిభుజాకార మాత్రిక.

  1. 1 మాత్రమే
  2. 2 మాత్రమే
  3. 1 మరియు 2
  4. పైవేవీ కాదు

Answer (Detailed Solution Below)

Option 3 : 1 మరియు 2
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Detailed Solution

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పద్ధతి:

ఎగువ త్రిభుజాకార మాత్రిక:

ఏదైనా చతురస్ర మాత్రిక, ప్రధాన వికర్ణం క్రింద ఉన్న ప్రతి మూలకం సున్నాగా ఉంటే అది ఎగువ త్రిభుజాకార మాత్రికగా చెప్పబడుతుంది.

ఉదా: ఇక్కడ, మనకు ఆర్డర్ 3, A యొక్క మాత్రిక A ఉంది = \(\left( {\begin{array}{*{20}{c}} a&b&c\\ 0&e&d\\ 0&0&f \end{array}} \right)\), ఇక్కడ a, b, c, d, e మరియు f ∈ R ఎగువ త్రిభుజాకార మాత్రిక.

దిగువ త్రిభుజాకార మాత్రిక:

ఏదైనా చతురస్ర మాత్రిక, ప్రధాన వికర్ణం పైన ఉన్న ప్రతి మూలకం సున్నాగా ఉంటే అది తక్కువ త్రిభుజాకార మాత్రికగా చెప్పబడుతుంది.

ఉదా: ఇక్కడ, మనకు ఆర్డర్ 3, A యొక్క మాత్రిక A ఉంది = \(\left( {\begin{array}{*{20}{c}} a&0&0\\ b&e&0\\ c&d&f \end{array}} \right)\), ఇక్కడ a, b, c, d, e మరియు f ∈ R దిగువ త్రిభుజాకార మాత్రిక.

గుర్తింపు మాత్రిక:

ఏదైనా చతురస్ర మాతృక, దాని ప్రధాన వికర్ణ మూలకాలు ఒకటి మరియు మిగిలిన మూలకాలు సున్నాగా ఉంటే అది గుర్తింపు మాత్రికగా చెప్పబడుతుంది.

ఉదా: ఇక్కడ, మనకు ఆర్డర్ 3, A యొక్క మాత్రిక I = \(\left( {\begin{array}{*{20}{c}} 1&0&0\\ 0&1&0\\ 0&0&1 \end{array}} \right)\), అనేది గుర్తింపు మాత్రిక.

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