Calculate the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 2

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Question: Calculate the determinant of the matrix \\( H = \\begin{pmatrix} 1 & 0 & 2 \\\\ 0 & 1 & 3 \\\\ 0 & 0 & 1 \\end{pmatrix} \\). (2020)

Options:

Correct Answer: 1

Solution:

The determinant of an upper triangular matrix is the product of its diagonal elements: \\( 1*1*1 = 1 \\).

Calculate the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \). (2020)

Calculate the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \). (2020)

Step 1: Identify the matrix H, which is given as H = [[1, 0, 2], [0, 1, 3], [0, 0, 1]].
Step 2: Recognize that H 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 H. The diagonal elements are 1, 1, and 1.
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 H.

Determinant of Upper Triangular Matrix – The determinant of an upper triangular matrix can be calculated by multiplying its diagonal elements.