What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \)? (2022)
Practice Questions
1 question
Q1
What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \)? (2022)
-14
14
0
6
Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \)? (2022)
Solution: Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).
Steps: 10
Step 1: Identify the matrix F, which is F = [[1, 2, 3], [0, 1, 4], [5, 6, 0]].
Step 2: Use the formula for the determinant of a 3x3 matrix: det(F) = a(ei - fh) - b(di - eg) + c(dh - eg), where the matrix is structured as follows: [[a, b, c], [d, e, f], [g, h, i]].
Step 3: Assign values from the matrix to the variables: a = 1, b = 2, c = 3, d = 0, e = 1, f = 4, g = 5, h = 6, i = 0.
Step 4: Calculate ei - fh: ei = 1*0 = 0 and fh = 4*6 = 24, so ei - fh = 0 - 24 = -24.
Step 5: Calculate di - eg: di = 0*0 = 0 and eg = 1*5 = 5, so di - eg = 0 - 5 = -5.
