Input interpretation
![lead(II) ions | formal charges](../image_source/6388773f62dbc53142ee171d6a89c6f6.png)
lead(II) ions | formal charges
Result
![(2)](../image_source/74ab3d523307fd66ff90b3244cec6b97.png)
(2)
Table
![2](../image_source/989065481850010e46151ea39b19ce63.png)
2
Characteristic polynomial
![2 - λ](../image_source/db760bede528377e525590ebc5951bc9.png)
2 - λ
Possible intermediate steps
![Find the characteristic polynomial of the matrix M with respect to the variable λ: M = (2) To find the characteristic polynomial of a matrix, subtract a variable multiplied by the identity matrix and take the determinant: left bracketing bar M - λ I right bracketing bar left bracketing bar M - λ I right bracketing bar | = | left bracketing bar 2 - λ 1 right bracketing bar | = | left bracketing bar 2 - λ right bracketing bar invisible comma = left bracketing bar 2 - λ right bracketing bar The determinant of a diagonal matrix is the product of its diagonal elements: left bracketing bar 2 - λ right bracketing bar 2 - λ = 2 - λ: Answer: | | 2 - λ](../image_source/cfdd8abe02fb84de0d0ea389968e9992.png)
Find the characteristic polynomial of the matrix M with respect to the variable λ: M = (2) To find the characteristic polynomial of a matrix, subtract a variable multiplied by the identity matrix and take the determinant: left bracketing bar M - λ I right bracketing bar left bracketing bar M - λ I right bracketing bar | = | left bracketing bar 2 - λ 1 right bracketing bar | = | left bracketing bar 2 - λ right bracketing bar invisible comma = left bracketing bar 2 - λ right bracketing bar The determinant of a diagonal matrix is the product of its diagonal elements: left bracketing bar 2 - λ right bracketing bar 2 - λ = 2 - λ: Answer: | | 2 - λ
Eigenvalues
![λ_1 = 2](../image_source/05a7cf1bb72c95096351a07e7f2b948c.png)
λ_1 = 2
Possible intermediate steps
![Find all the eigenvalues of the matrix M: M = (2) Find λ element C such that M v = λ v for some nonzero vector v: M v = λ v The only value of λ for which M v = λ v for any nonzero v is 2: Answer: | | 2](../image_source/7a0217f1c1568cffc000f1ccc3346ecc.png)
Find all the eigenvalues of the matrix M: M = (2) Find λ element C such that M v = λ v for some nonzero vector v: M v = λ v The only value of λ for which M v = λ v for any nonzero v is 2: Answer: | | 2
Eigenvectors
![v_1 = (1)](../image_source/9e5c4a60cf82e02b12875b93a4b0f5ef.png)
v_1 = (1)
Possible intermediate steps
![Find all the eigenvalues and eigenvectors of the matrix M: M = (2) Find λ element C such that M v = λ v for some nonzero vector v: M v = λ v The only value of λ for which M v = λ v for any nonzero v is 2: 2 The equation M v = λ v is satisfied by each v element C^1, which means a suitable eigenvalue/eigenvector pair is: Answer: | | Eigenvalue | Eigenvector 2 | (1)](../image_source/cc056998238c0eaf222a043be5c135f6.png)
Find all the eigenvalues and eigenvectors of the matrix M: M = (2) Find λ element C such that M v = λ v for some nonzero vector v: M v = λ v The only value of λ for which M v = λ v for any nonzero v is 2: 2 The equation M v = λ v is satisfied by each v element C^1, which means a suitable eigenvalue/eigenvector pair is: Answer: | | Eigenvalue | Eigenvector 2 | (1)