For the matrix \( B = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \), what is the determinant \( |B| \)?
Practice Questions
1 question
Q1
For the matrix \( B = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \), what is the determinant \( |B| \)?
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The determinant is 0 because the rows are linearly dependent.
Questions & Step-by-step Solutions
1 item
Q
Q: For the matrix \( B = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \), what is the determinant \( |B| \)?
Solution: The determinant is 0 because the rows are linearly dependent.
Steps: 7
Step 1: Identify the matrix B, which is given as B = [[1, 2], [2, 4]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is |B| = ad - bc, where a, b, c, and d are the elements of the matrix arranged as follows: [[a, b], [c, d]].
Step 3: In our matrix B, a = 1, b = 2, c = 2, and d = 4.
Step 4: Substitute the values into the determinant formula: |B| = (1 * 4) - (2 * 2).
Step 5: Calculate the products: 1 * 4 = 4 and 2 * 2 = 4.
Step 6: Subtract the second product from the first: 4 - 4 = 0.
