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If \( C = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 &a

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Question: If \\( C = \\begin{pmatrix} 1 & 0 & 2 \\\\ 0 & 1 & 3 \\\\ 0 & 0 & 1 \\end{pmatrix} \\), what is the determinant of C? (2022)

Options:

  1. 0
  2. 1
  3. 2
  4. 3

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.

If \( C = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 &a

Practice Questions

Q1
If \( C = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \), what is the determinant of C? (2022)
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

If \( C = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \), what is the determinant of C? (2022)
  • Step 1: Identify the matrix C, which is given as C = [[1, 0, 2], [0, 1, 3], [0, 0, 1]].
  • Step 2: Recognize that C 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 C. The diagonal elements are 1, 1, and 1.
  • Step 4: Calculate the product of the diagonal elements: 1 * 1 * 1.
  • Step 5: The result of the product is 1, which is the determinant of the matrix C.
  • Determinant of Upper Triangular Matrix – The determinant of an upper triangular matrix is calculated by multiplying its diagonal elements.
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