Pertanyaan

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

Solusi

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Jawaban

### Nilai eigen dari matriks adalah .

Penjelasan

## Step 1: Identify the Type of Matrix### The given matrix is a 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 , where are the diagonal elements.## Step 3: Extract Diagonal Elements### The diagonal elements of the matrix are: - First row, first column: - Second row, second column: - Third row, third column: - Fourth row, fourth column: ## Step 4: List the Eigenvalues### Therefore, the eigenvalues of the matrix are the diagonal elements: .