What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?
Practice Questions
1 question
Q1
What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?
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The determinant is 0 because the rows are linearly dependent.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?
Solution: The determinant is 0 because the rows are linearly dependent.
Steps: 7
Step 1: Identify the matrix. The given matrix is \( \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \).
Step 2: Recall the formula for the determinant of a 2x2 matrix. For a matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), the determinant is calculated as \( ad - bc \).
Step 3: Assign values from the matrix to the variables: Here, \( a = 1 \), \( b = 2 \), \( c = 2 \), and \( d = 4 \).
Step 4: Plug the values into the determinant formula: Calculate \( 1 \cdot 4 - 2 \cdot 2 \).
Step 5: Perform the multiplication: \( 1 \cdot 4 = 4 \) and \( 2 \cdot 2 = 4 \).
Step 6: Subtract the results: \( 4 - 4 = 0 \).
Step 7: Conclude that the determinant of the matrix is 0.
