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Calculate the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 2
Calculate the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \). (2020)
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Calculate the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \). (2020)
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The determinant of an upper triangular matrix is the product of its diagonal elements: \( 1*1*1 = 1 \).
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Q: Calculate the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \). (2020)
Solution:
The determinant of an upper triangular matrix is the product of its diagonal elements: \( 1*1*1 = 1 \).
Steps: 5
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Step 1: Identify the matrix H, which is given as H = [[1, 0, 2], [0, 1, 3], [0, 0, 1]].
Step 2: Recognize that H 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 H. The diagonal elements are 1, 1, and 1.
Step 4: Calculate the product of the diagonal elements. Multiply 1 * 1 * 1.
Step 5: The result of the multiplication is 1, which is the determinant of the matrix H.
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