If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |2
Practice Questions
Q1
If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |2A| \)?
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8
4
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Questions & Step-by-Step Solutions
If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |2A| \)?
Step 1: Identify the matrix A, which is A = [[1, 2], [3, 4]].
Step 2: Calculate the determinant of A, denoted as |A|. The formula for the determinant of a 2x2 matrix [[a, b], [c, d]] is ad - bc.
Step 3: For matrix A, a = 1, b = 2, c = 3, d = 4. So, |A| = (1 * 4) - (2 * 3) = 4 - 6 = -2.
Step 4: Now, we need to find the determinant of 2A. The matrix 2A is obtained by multiplying each element of A by 2, resulting in 2A = [[2*1, 2*2], [2*3, 2*4]] = [[2, 4], [6, 8]].
Step 5: The determinant of 2A can be calculated using the property of determinants: |kA| = k^n * |A|, where k is a scalar and n is the size of the matrix. Here, k = 2 and n = 2 (since A is 2x2).
