SOLUTION: Hello, I would greatly appreciate it if a tutor could please verify my work for the below problem. Find the determinant of the matrix B = [-1, 2, 3, 6, 0, 2, 3, 5, 1]. M

Question 12425: Hello,

I would greatly appreciate it if a tutor could please verify my work for the below problem.

Find the determinant of the matrix B = [-1, 2, 3, 6, 0, 2, 3, 5, 1]. Matrix B is a 3x3 square matrix. The first column is -1, 2, 3. The second column is 6, 0, 2. The third column in 3, 5, 1. Row 1 is -1, 6, 3. Row 2 is 2, 0 , 5. Row 3 is 3, 2, 1.

I started by taking the numbers of the first row (-1, 6, 3) and multiplying them by the 2x2 matrix that remains when the row and column each number is in is deleted.
det B = -1[(0)(1)-(5)(2)] - 6[(2)(1)-(5)(3)] + 3[(2)(2)-(0)(3)]
det B = -1(0-10) - 6(2-15) + 3(4 - 0)
det B = -1(-10) - 6(-13) + 3(4)
det B = 10 + 78 + 12
det B = 100

In advance, thank you for your assistance!

Answer by khwang(438) (Show Source):
You can put this solution on YOUR website!
B =
[-1 6 3 ]
[ 2 0 5]
[ 3 2 1]
You did a good job and the answer is correct.
But, wy not expanding along the 2nd row ,since it contains 0.
det(B) = -2(6-6) - 5(-2 -18) = 100
Also,you typed too many redundant 0's and repetitive det(B) in
your solution. Such as
det B = -1(0-10) - 6(2-15) + 3(4 - 0)
It seems that you don't have enough confdence in yourself.
[Try to use your eyes and mind to calculate small numbers
instead of using pen, or other tools.]

I am a very lazy person,that is why I am always looking for the
shortest cut to solve the problems.
Kenny