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ম্যাট্রিক্সের আইগেনমান (Eigenvalues) হল :

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MP HSTET Varg 1 - 2018 (Mathematics) Held on 6th Feb 2019 Shift 2
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  1. 1, −4, 7
  2. 1, 4, 7
  3. 1, 4, −7
  4. −1, −4, 7

Answer (Detailed Solution Below)

Option 1 : 1, −4, 7
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Detailed Solution

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প্রদত্ত:

3 x 3 ক্রমের বর্গ ম্যাট্রিক্স হল

ধারণা:

একটি ম্যাট্রিক্সের আইগেনমান (eigenvalue) নির্ণয় করার জন্য, নিম্নলিখিত কাজগুলি করুন:
1 - যাচাই করুন যে নির্দিষ্ট ম্যাট্রিক্স A একটি বর্গ ম্যাট্রিক্স। একই ক্রমের অভেদ ম্যাট্রিক্স I নির্ণয় করুন।
2 - ম্যাট্রিক্স গণনা করুন, যেখানে একটি স্কেলার মান।
3 - ম্যাট্রিক্স এর নির্ণায়ক (determinant) নির্ণয় করুন এবং এটিকে শূন্যের সমান করুন।
4 - সৃষ্ট সমীকরণ থেকে A এর সম্ভাব্য সমস্ত মান নির্ণয় করুন, যা ম্যাট্রিক্স A এর প্রয়োজনীয় আইগেনমান।

সমাধান:

সুতরাং, বিকল্প 1 সঠিক।

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