Tentukan nilai eigen dari matriks [ A=[ 1 & 2 & 3 & 4 0 & -1 & 3 & 4 0 & 0 & -1 & 4 0 & 0 & 0 & 1 ] ]

Question

Pertanyaan

Tentukan nilai eigen dari matriks [ A=[ 1 & 2 & 3 & 4 0 & -1 & 3 & 4 0 & 0 & -1 & 4 0 & 0 & 0 & 1 ] ]

Tampilkan lebih banyak

Answer 1

Nilai eigen dari matriks adalah $1, -1, -1, 1$.

Answer 2

Step 1:

Identify the Type of Matrix

The given matrix is a $4 \times 4$ upper triangular matrix. In an upper triangular matrix, all elements below the main diagonal are zero.

Step 2:

Determine Eigenvalues of an Upper Triangular Matrix

For an upper triangular matrix, the eigenvalues are simply the entries on the main diagonal. This is because the characteristic polynomial of an upper triangular matrix is the product of $(\lambda - a_{ii})$, where $a_{ii}$ are the diagonal elements.

Step 3:

Extract Diagonal Elements

The diagonal elements of the matrix $A$ are:

- First row, first column: $1$
- Second row, second column: $-1$
- Third row, third column: $-1$
- Fourth row, fourth column: $1$

Step 4:

List the Eigenvalues

Therefore, the eigenvalues of the matrix $A$ are the diagonal elements:

$1, -1, -1, 1$.

Pertanyaan

Tentukan nilai eigen dari matriks [ A=[ 1 & 2 & 3 & 4 0 & -1 & 3 & 4 0 & 0 & -1 & 4 0 & 0 & 0 & 1 ] ]

Jawaban

Penjelasan

Step 1:

Step 2:

Step 3:

Step 4:

Pertanyaan Panas lebih