Find the determinant of the matrix \( D = \begin{pmatrix} 1 & 0 & 2 \\ 0

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Question: Find the determinant of the matrix \\( D = \\begin{pmatrix} 1 & 0 & 2 \\\\ 0 & 1 & 3 \\\\ 0 & 0 & 1 \\end{pmatrix} \\).

Options:

Correct Answer: 1

Solution:

The determinant of an upper triangular matrix is the product of its diagonal elements, which is 1.

Find the determinant of the matrix \( D = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \).

Find the determinant of the matrix \( D = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \).

Step 1: Identify the matrix D, which is given as D = [[1, 0, 2], [0, 1, 3], [0, 0, 1]].
Step 2: Recognize that D is an upper triangular matrix. This means all the elements below the main diagonal are zero.
Step 3: Find the diagonal elements of the matrix D. The diagonal elements are 1 (first row), 1 (second row), and 1 (third row).
Step 4: Calculate the product of the diagonal elements. Multiply 1 * 1 * 1.
Step 5: The result of the multiplication is 1, which is the determinant of the matrix D.

Determinant of a Matrix – The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties about the matrix, such as whether it is invertible.
Upper Triangular Matrix – An upper triangular matrix is a type of square matrix where all the entries below the main diagonal are zero. The determinant of such a matrix is the product of its diagonal elements.