PYQs Based Test - 02 : Eigenvalues and Eigenvectors

Topics Covered

Sample Questions from this Test

1. In the matrix equation $[A]\{X\}=\{R\}$,
   
   [A] = 4 & 8 & 4\
   4pt]
   8 & 16 & -4\
   4pt] 4 & -4 & 15 , \ = 2\
   4pt]
   1\
   4pt] 4 , \ = 32\
   4pt]
   16\
   4pt] 64 .
   
   **One of the eigenvalues of the matrix $[A]$ is:**
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2. Let the eigenvalues of a 2 × 2 matrix A be 1, -2 with eigenvectors x₁ and x₂ respectively. Then the eigenvalues and eigenvectors of the matrix A³ would, respectively, be
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3. Let I be a 100-dimensional identity matrix and E be the set of its distinct (no value appears more than once in E) real eigenvalues. The number of elements in E is .
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Test Instructions

• The test contains 10 questions and a total of 16 marks.
• You will have 180 minutes to complete the test. The timer cannot be paused once started.
• Negative marking: 0.25 mark(s) deducted per wrong answer.
• Use the question palette to mark questions for review and navigate freely.
• Detailed solutions and analytics are available immediately after submission.
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