What is the value of \( |H| \) for \( H = \begin{pmatrix} 1 & 0 \\ 0 & 1

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Question: What is the value of \\( |H| \\) for \\( H = \\begin{pmatrix} 1 & 0 \\\\ 0 & 1 \\end{pmatrix} \\)? (2021)

Options:

Correct Answer: 1

Exam Year: 2021

Solution:

The determinant of the identity matrix is always 1.

What is the value of \( |H| \) for \( H = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \)? (2021)

What is the value of \( |H| \) for \( H = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \)? (2021)

Step 1: Identify the matrix H, which is given as H = [[1, 0], [0, 1]].
Step 2: Recognize that this matrix is the identity matrix.
Step 3: Understand that the determinant of the identity matrix is always 1, regardless of its size.
Step 4: Conclude that the value of |H|, which represents the determinant of matrix H, is 1.

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