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

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Question: What is the determinant of the matrix \\( H = \\begin{pmatrix} 1 & 2 \\\\ 2 & 4 \\end{pmatrix} \\)?

Options:

Correct Answer: 0

Solution:

The determinant is 0 because the rows are linearly dependent.

What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?

What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?

Step 1: Identify the matrix H, which is given as H = [[1, 2], [2, 4]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is det(H) = (a * d) - (b * c), where the matrix is [[a, b], [c, d]].
Step 3: In our matrix H, a = 1, b = 2, c = 2, and d = 4.
Step 4: Substitute the values into the determinant formula: det(H) = (1 * 4) - (2 * 2).
Step 5: Calculate the first part: 1 * 4 = 4.
Step 6: Calculate the second part: 2 * 2 = 4.
Step 7: Subtract the second part from the first part: 4 - 4 = 0.
Step 8: Conclude that the determinant of the matrix H is 0.

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