What is the determinant of the matrix $((-3,5,7),(0,1,2),(-1,1,4))$ ?

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Answer 1 · 2017-10-05T12:30:16

The answer is $=-9$

The matrix is

$((-3,5,7),(0,1,2),(-1,1,4))$

Perform the following operations on the rows

$R3larrR3-1/3R1$

$((-3,5,7),(0,1,2),(0,-2/3,5/3))$

$R3larrR3+2/3R2$

$((-3,5,7),(0,1,2),(0,0,3))$

The determinant is

$|(-3,5,7),(0,1,2),(0,0,3)| =-3*1*3$

$=-9$

What is the determinant of the matrix ((-3,5,7),(0,1,2),(-1,1,4))((-3,5,7),(0,1,2),(-1,1,4)) ?