, MAT3700 Assignment 3 (COMPLETE
ANSWERS)2024 - DUE 28 August 2024 ; 100%
TRUSTED Complete, trusted solutions and
explanations.
QUESTION 1 If 3 6 1 4 B , find the eigenvalues of B.
(5)
To find the eigenvalues of the matrix B=(3614), we will follow a
systematic approach.
Step 1: Define Eigenvalues
Eigenvalues of a matrix are found by solving the characteristic
equation, which is derived from the determinant of B−λI=0,
where I is the identity matrix and λ represents the eigenvalue.
Step 2: Set Up the Characteristic Equation
For our matrix B:B−λI=(3−λ614−λ)
Step 3: Calculate the Determinant
Next, we calculate the determinant of this
matrix:det(B−λI)=(3−λ)(4−λ)−(6)(1)Expanding this gives: [ = (3 - \
lambda)(4 - \lambda) - 6 = (12 - 4\lambda - 3\lambda + \
lambda^2) - 6 = \lambda^2 - 7\lambda + 6 ]
Step 4: Solve for Eigenvalues
Now, we set the determinant equal to zero to find the
eigenvalues:λ2−7λ+6=0
ANSWERS)2024 - DUE 28 August 2024 ; 100%
TRUSTED Complete, trusted solutions and
explanations.
QUESTION 1 If 3 6 1 4 B , find the eigenvalues of B.
(5)
To find the eigenvalues of the matrix B=(3614), we will follow a
systematic approach.
Step 1: Define Eigenvalues
Eigenvalues of a matrix are found by solving the characteristic
equation, which is derived from the determinant of B−λI=0,
where I is the identity matrix and λ represents the eigenvalue.
Step 2: Set Up the Characteristic Equation
For our matrix B:B−λI=(3−λ614−λ)
Step 3: Calculate the Determinant
Next, we calculate the determinant of this
matrix:det(B−λI)=(3−λ)(4−λ)−(6)(1)Expanding this gives: [ = (3 - \
lambda)(4 - \lambda) - 6 = (12 - 4\lambda - 3\lambda + \
lambda^2) - 6 = \lambda^2 - 7\lambda + 6 ]
Step 4: Solve for Eigenvalues
Now, we set the determinant equal to zero to find the
eigenvalues:λ2−7λ+6=0
