What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 0 & 2 \

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Question: What is the determinant of the matrix \\( F = \\begin{pmatrix} 1 & 0 & 2 \\\\ 0 & 1 & 3 \\\\ 0 & 0 & 1 \\end{pmatrix} \\)? (2022)

Options:

Correct Answer: 1

Exam Year: 2022

Solution:

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

What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \)? (2022)

What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \)? (2022)

Step 1: Identify the matrix F, which is given as F = (1 0 2; 0 1 3; 0 0 1).
Step 2: Recognize that this matrix 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. 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 F.

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