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Calculate the determinant of \( I = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{
Calculate the determinant of \( I = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2022)
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Calculate the determinant of \( I = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2022)
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12
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The determinant is calculated as \( 3*4 - 2*1 = 12 - 2 = 10 \).
Questions & Step-by-step Solutions
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Q
Q: Calculate the determinant of \( I = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2022)
Solution:
The determinant is calculated as \( 3*4 - 2*1 = 12 - 2 = 10 \).
Steps: 7
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Step 1: Identify the elements of the matrix I = \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). The elements are: a = 3, b = 2, c = 1, d = 4.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is given by \( \text{det}(I) = a \cdot d - b \cdot c \).
Step 3: Substitute the values into the formula: \( \text{det}(I) = 3 \cdot 4 - 2 \cdot 1 \).
Step 4: Calculate the first part: \( 3 \cdot 4 = 12 \).
Step 5: Calculate the second part: \( 2 \cdot 1 = 2 \).
Step 6: Subtract the second part from the first part: \( 12 - 2 = 10 \).
Step 7: Conclude that the determinant of the matrix I is 10.
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