What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \)?
Practice Questions
1 question
Q1
What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \)?
-1
1
2
3
The determinant is calculated as \( 1*5 - 2*3 = 5 - 6 = -1 \).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \)?
Solution: The determinant is calculated as \( 1*5 - 2*3 = 5 - 6 = -1 \).
Steps: 7
Step 1: Identify the elements of the matrix. The matrix is \( \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \). The elements are: a = 1, b = 2, c = 3, d = 5.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is \( ad - bc \).
Step 3: Substitute the values into the formula: \( 1*5 - 2*3 \).
Step 4: Calculate \( 1*5 \) which equals 5.
Step 5: Calculate \( 2*3 \) which equals 6.
Step 6: Subtract the second result from the first: \( 5 - 6 \).
Step 7: The result is -1, so the determinant of the matrix is -1.
