Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 & 1 \\ 1 & 0 & 2 \\ 4 & 1 & 0 \end{pmatrix} \).
Practice Questions
1 question
Q1
Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 & 1 \\ 1 & 0 & 2 \\ 4 & 1 & 0 \end{pmatrix} \).
-10
10
0
5
Using the determinant formula, we find it equals 10.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 & 1 \\ 1 & 0 & 2 \\ 4 & 1 & 0 \end{pmatrix} \).
Solution: Using the determinant formula, we find it equals 10.
Steps: 9
Step 1: Identify the matrix. We have the matrix A = \( \begin{pmatrix} 2 & 3 & 1 \\ 1 & 0 & 2 \\ 4 & 1 & 0 \end{pmatrix} \).
Step 2: Write down the formula for the determinant of a 3x3 matrix. The formula is: \( \text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg) \), where the matrix is \( \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} \).
Step 3: Assign values from the matrix to the variables in the formula. Here, a = 2, b = 3, c = 1, d = 1, e = 0, f = 2, g = 4, h = 1, i = 0.
Step 4: Calculate the parts of the formula. First, calculate ei - fh: 0*0 - 2*1 = 0 - 2 = -2.
