What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)? (2021)
Practice Questions
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Q1
What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)? (2021)
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The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).
Questions & Step-by-step Solutions
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Q
Q: What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)? (2021)
Solution: The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).
Steps: 6
Step 1: Identify the elements of the matrix A. The matrix A is given as A = [[1, 2], [3, 4]]. Here, a = 1, b = 2, c = 3, and d = 4.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is det(A) = ad - bc.
Step 3: Substitute the values into the formula. Calculate a * d = 1 * 4 = 4.
Step 4: Calculate b * c = 2 * 3 = 6.
Step 5: Now, subtract the second result from the first: 4 - 6 = -2.
