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Let A be the 2 X 2 matrix with elements a11 = 2, a12 = 3, a21 = 1 and a22 = 4 then the Characteristic Equation:?

  • a)
    λ2 − 6λ + 5

  • b)
    λ2 + 6λ + 5

  • c)
    λ2 − 6λ − 5

  • d)
    λ2 + 6λ + 5

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let A be the 2 X 2 matrix with elements a11= 2, a12= 3, a21=1 and a22=...
Given Matrix:



Characteristic Equation:



(2−λ) (4−λ) −3 = 0


λ2 − 6λ + 5 = 0


λ = 5 or λ = 1
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Most Upvoted Answer
Let A be the 2 X 2 matrix with elements a11= 2, a12= 3, a21=1 and a22=...

Calculation of Eigenvalues:

Eigenvalues of a matrix are the values of λ that satisfy the equation det(A - λI) = 0, where A is the given matrix, I is the identity matrix, and det() represents the determinant of a matrix.

Given Matrix A:
A = | 2 3 |
| 1 4 |

Calculating determinant of A - λI:
A - λI = | 2-λ 3 |
| 1 4-λ |

det(A - λI) = (2-λ)(4-λ) - (1)(3) = λ^2 - 6λ + 5

Solving the quadratic equation for eigenvalues:
Setting det(A - λI) = 0:
λ^2 - 6λ + 5 = 0
(λ - 5)(λ - 1) = 0

Therefore, the eigenvalues are λ = 5 and λ = 1.

Final Answer:
Hence, the eigenvalues of the given matrix A are 5 and 1. Therefore, the correct answer is option 'A' - 3125 and 1.
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Let A be the 2 X 2 matrix with elements a11= 2, a12= 3, a21=1 and a22= 4 then the Characteristic Equation:?a)λ2 − 6λ + 5b)λ2+ 6λ + 5c)λ2 − 6λ− 5d)λ2+ 6λ + 5Correct answer is option 'A'. Can you explain this answer?
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