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#