SOLUTION: if we know that det(A) =2 where A = 0 1 0 1 0 1 1 1 0 USE THE PROPERTIES OF DETERMINANT ( And the info a

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Question 376385: if we know that det(A) =2 where A = 0 1 0
1 0 1
1 1 0
USE THE PROPERTIES OF DETERMINANT ( And the info about det(A) given) to find the determinant of B = 0 ab^2 ac^2
a^2b 0 bc^2
a^2c b^2c 0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
det%28%28matrix%283%2C3%2C0%2C1%2C1%2C1%2C0%2C1%2C1%2C1%2C0%29%29+%29=+2.
We have to get
Now factor a%5E2 from the 1st column, b%5E2 from the 2nd column, and c%5E2 from the 3rd column, to get
a%5E2b%5E2c%5E2det%28%28matrix%283%2C3%2C0%2Ca%2Ca%2Cb%2C0%2Cb%2Cc%2Cc%2C0%29%29%29.
Then factor a from the 1st row, b from the 2nd row, and c from the 3rd row, to get
a%5E3b%5E3c%5E3det%28%28matrix%283%2C3%2C0%2C1%2C1%2C1%2C0%2C1%2C1%2C1%2C0%29%29%29.
Therefore the value of the determinant is 2a%5E3b%5E3c%5E3.