SOLUTION: Find the determinant A [-7 2 -1 ] 0 -3 -1 3 -4 -2

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Question 1148752: Find the determinant
A [-7 2 -1 ]
0 -3 -1
3 -4 -2
Answer by ikleyn(52829) About Me  (Show Source):
You can put this solution on YOUR website!
.

    A = %28matrix%283%2C3%2C+-7%2C2%2C-1%2C+++0%2C-3%2C-1%2C++3%2C-4%2C-2%29%29.


Multiply the third column of the matrix A by 2 and add it to the second column. You will get the matrix B then


    B = %28matrix%283%2C3%2C+-7%2C0%2C-1%2C+++0%2C-5%2C-1%2C++3%2C-8%2C-2%29%29.


The basic property of the determinant is that under such transformations of the matrix, determinant remains the same:


    det(B) = det(A).


Now determinant B is easier to calculate than determinant A.  Omitting the zero terms,


     det(B) = (-7)*(-5)*(-2) - 3*(-5)*(-1) - (-7)*(-8)*(-1) = -29.    ANSWER

Solved.