What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 0 \\ 0 &

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Question: What is the determinant of the matrix \\( C = \\begin{pmatrix} 5 & 0 \\\\ 0 & 7 \\end{pmatrix} \\)? (2020)

Options:

Correct Answer: 35

Exam Year: 2020

Solution:

The determinant of a diagonal matrix is the product of its diagonal elements: \\( 5*7 = 35 \\).

What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 0 \\ 0 & 7 \end{pmatrix} \)? (2020)

What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 0 \\ 0 & 7 \end{pmatrix} \)? (2020)

Step 1: Identify the matrix C, which is given as C = (5 0; 0 7).
Step 2: Recognize that this is a diagonal matrix, meaning all non-diagonal elements are zero.
Step 3: Understand that the determinant of a diagonal matrix is calculated by multiplying the diagonal elements together.
Step 4: Multiply the diagonal elements: 5 (from the first row) and 7 (from the second row).
Step 5: Calculate the product: 5 * 7 = 35.
Step 6: Conclude that the determinant of the matrix C is 35.

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