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

Practice Questions

Q1
What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 0 \\ 0 & 7 \end{pmatrix} \)? (2020)
  1. 35
  2. 12
  3. 0
  4. 5

Questions & Step-by-Step Solutions

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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