If I = [[1, 0, 2], [0, 1, 3], [1, 1, 0]], find det(I). (2023)
Practice Questions
Q1
If I = [[1, 0, 2], [0, 1, 3], [1, 1, 0]], find det(I). (2023)
-1
0
1
2
Questions & Step-by-Step Solutions
If I = [[1, 0, 2], [0, 1, 3], [1, 1, 0]], find det(I). (2023)
Step 1: Identify the matrix I. The matrix I is [[1, 0, 2], [0, 1, 3], [1, 1, 0]].
Step 2: Write down the formula for the determinant of a 3x3 matrix. The formula is: det(I) = a(ei - fh) - b(di - fg) + c(dh - eg), where the matrix is [[a, b, c], [d, e, f], [g, h, i]].
Step 3: Assign values from the matrix to the variables in the formula. Here, a=1, b=0, c=2, d=0, e=1, f=3, g=1, h=1, i=0.
Step 4: Substitute the values into the determinant formula: det(I) = 1(1*0 - 3*1) - 0(0 - 3*1) + 2(0 - 1*1).
Step 5: Calculate each part of the formula: 1(0 - 3) = 1 * -3 = -3, 0(0 - 3) = 0, and 2(0 - 1) = 2 * -1 = -2.
Determinant of a 3x3 Matrix – The determinant of a 3x3 matrix can be calculated using the formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where A = [[a, b, c], [d, e, f], [g, h, i]].
Matrix Operations – Understanding how to perform basic operations such as multiplication and addition of matrix elements is crucial for calculating determinants.
