The Characteristic Polynomial of a 5 × 5 Matrix Is $\lambda ^ { 5 } - 24 \lambda ^ { 4 } + 189 \lambda ^ { 3 } - 486 \lambda ^ { 2 }$

question 4

Multiple Choice

The characteristic polynomial of a 5 × 5 matrix is given below. Find the eigenvalues and their multiplicities.
- $\lambda ^ { 5 } - 24 \lambda ^ { 4 } + 189 \lambda ^ { 3 } - 486 \lambda ^ { 2 }$

• A) 0 (multiplicity 2), 9 (multiplicity 2), 6 (multiplicity 1 )
• B) 0 (multiplicity 2), \(- 9\) (multiplicity 2), -6 (multiplicity 1)
• C) 0 (multiplicity 2), \(- 9\) (multiplicity 2), 6 (multiplicity 1 )
• D) 0 (multiplicity 1), 9 (multiplicity \(3 ), 6\) (multiplicity 1 )

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Definitions:

Calorie

A unit for measuring the heat value of food.

Heat Value

The amount of heat produced by the complete combustion of a given substance, often measured in Joules per kilogram (J/kg) or British Thermal Units (BTU).

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any nutritious substance that people or animals eat or drink to maintain life and growth.

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Illness, disease.