Cayley-Hamilton Theorem Definition, Equation & Example


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question 1 of 3

The Caley-Hamilton theorem deals only with _____.

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1. In a square matrix, the number of rows and the number of columns are _____.

2. A 2-by-2 matrix has 2 and 3 in the first row; 0 and 1 in the second row. Calculate the characteristic polynomial p(λ).

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About This Quiz & Worksheet

The Cayley-Hamilton theorem is the main topic of this combination of a quiz and worksheet. You are asked about what the theorem deals with and how to apply the theorem to a given problem.

Quiz & Worksheet Goals

Expect to see the following topics appearing in the quiz questions:

  • The shapes dealt with by the Cayley-Hamilton theorem
  • Calculating a characteristic polynomial
  • An equation resulting from the use of the theorem
  • Finding an inverse matrix

Skills Practiced

  • Defining key concepts - ensure that you can name the type of matrices associated with the Cayley-Hamilton theorem
  • Information recall - remember what you have learned about inverse matrices
  • Problem solving - use what you know to solve practice problems involving characteristic polynomials

Additional Learning

For extra studies with the theorem, go to the lesson titled Cayley-Hamilton Theorem Definition, Equation & Example. With it, you can access the following additional content:

  • Identity matrices
  • Determinants
  • Matrix multiplication