Question: Find the determinant of the matrix \\( \\begin{pmatrix} 2 & 3 \\\\ 1 & 4 \\end{pmatrix} \\).
Options:
5
6
7
8
Correct Answer: 5
Solution:
The determinant is \\( 2*4 - 3*1 = 8 - 3 = 5 \\).
Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \en
Practice Questions
Q1
Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \).
5
6
7
8
Questions & Step-by-Step Solutions
Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \).
Correct Answer: 5
Step 1: Identify the elements of the matrix. The matrix is \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \). The elements are: a = 2, b = 3, c = 1, d = 4.
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. Here, a = 2, b = 3, c = 1, d = 4. So, we calculate: \( 2*4 - 3*1 \).
Step 4: Calculate \( 2*4 \) which equals 8.
Step 5: Calculate \( 3*1 \) which equals 3.
Step 6: Subtract the second result from the first: \( 8 - 3 \) which equals 5.
Step 7: The determinant of the matrix is 5.
Determinant Calculation – Understanding how to compute the determinant of a 2x2 matrix using the formula ad - bc.
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