Question: What is the determinant of the matrix \\( \\begin{pmatrix} 5 & 6 \\\\ 7 & 8 \\end{pmatrix} \\)?
Options:
-2
2
1
0
Correct Answer: -2
Solution:
The determinant is calculated as \\( 5*8 - 6*7 = 40 - 42 = -2 \\).
What is the determinant of the matrix \( \begin{pmatrix} 5 & 6 \\ 7 & 8
Practice Questions
Q1
What is the determinant of the matrix \( \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)?
-2
2
1
0
Questions & Step-by-Step Solutions
What is the determinant of the matrix \( \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)?
Step 1: Identify the elements of the matrix. The matrix is \( \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \). The elements are: a = 5, b = 6, c = 7, d = 8.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is given by \( ad - bc \).
Step 3: Substitute the values into the formula: \( 5*8 - 6*7 \).
Step 4: Calculate \( 5*8 \) which equals 40.
Step 5: Calculate \( 6*7 \) which equals 42.
Step 6: Subtract the second result from the first: \( 40 - 42 \).
Step 7: The result is -2, which is the determinant of the matrix.
No concepts available.
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