What is the determinant of the matrix \( I = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \)? (2021)
Practice Questions
1 question
Q1
What is the determinant of the matrix \( I = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \)? (2021)
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12
The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the determinant of the matrix \( I = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \)? (2021)
Solution: The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).
Steps: 7
Step 1: Identify the elements of the matrix I. The matrix is I = (4, 2; 1, 3), which means it has 4 in the first row and first column, 2 in the first row and second column, 1 in the second row and first column, and 3 in the second row and second column.
Step 2: Use the formula for the determinant of a 2x2 matrix. The formula is: determinant = (first element * second element of the second row) - (second element * first element of the second row).
Step 3: Plug in the values from the matrix into the formula. Here, the first element is 4, the second element of the second row is 3, the second element is 2, and the first element of the second row is 1.
Step 4: Calculate the first part of the formula: 4 * 3 = 12.
Step 5: Calculate the second part of the formula: 2 * 1 = 2.
Step 6: Subtract the second part from the first part: 12 - 2 = 10.
