Question
In: Advanced Math
The determinant of a matrix is the product of its eigenvalues. Can you prove this when...
The determinant of a matrix is the product of its eigenvalues. Can you prove this when A is diagonalizable? How about if A is 2 x 2, and may or may not be diagonalizable? (Hint: What's the constant term in the characteristic polynomial>
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Prove: An (n × n) matrix A is not invertible ⇐⇒ one of the eigenvalues of...
Prove: An (n × n) matrix A is not invertible ⇐⇒ one of the
eigenvalues of A is λ = 0
Find the adjoint of matrix A, the determinant of matrix A, and the determinant of the...
Find the adjoint of matrix A, the determinant of matrix A, and
the determinant of the adjoint A.
A= 1 1 0 2
2 1 1 0
0 2 1 1
1 0 2 1
The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue...
The eigenvalues of the coefficient matrix can be found by
inspection or factoring. Apply the eigenvalue method to find a
general solution of the system.
x'1 = 6x1 + 6x2 +
2x3
x'2 = -8x1 - 8x2 -
6x3
x'3 = 8x1 + 8x2 +
6x3
What is the general solution in matrix form?
x(t) =
Find the eigenvalues and eigenvectors of the following matrix. Justify if its diagonaliazble or not. 1...
Find the eigenvalues and eigenvectors of the following matrix.
Justify if its diagonaliazble or not.
1 2 0
-3 2 3
-1 2 2
If you had a routine for computing all of the eigenvalues of a nonsymmetric matrix, how...
If you had a routine for computing all of the eigenvalues of a
nonsymmetric matrix, how could you use it to compute the roots of
any polynomial?
Matlab You will write a function to calculate the determinant of a matrix. It should work...
Matlab
You will write a function to calculate the determinant of a
matrix. It should work for any size matrix. Remember that the
determinant can be calculated by multiplying the diagonal elements
of an upper right triangular matrix. Your function will take a
matrix passed to it and put it in upper right triangular form. You
will work down the diagonal beginning at row 1 column 1, then row 2
column 2, etc. Note that the row and column numbers...
Find all eigenvalues and their corresponding eigenspaces of the following matrix.
Find all eigenvalues and their corresponding eigenspaces of the following matrix. B=\( \begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} \)
Find all eigenvalues and their corresponding eigenspaces of the following matrix.
Find all eigenvalues and their corresponding eigenspaces of the following matrix. A.\( \begin{pmatrix}3&0\\ 1&2\end{pmatrix} \)
Is there a relation between the determinant of the matrix associated to a linear mapping and...
Is there a
relation between the determinant of the matrix associated to a
linear mapping and the bijection of the mapping?
In economics, What is the role or function of the Determinant of a Vandermonde Matrix?
In economics, What is the role or function of the Determinant of
a Vandermonde Matrix?
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