How to evaluate the determinant of the given matrix by reducing the matrix to row echelon form ? first row ( 0 3 1 ) second row ( 1 1 2 ) and third row ( 3 2 4 )

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Answer 1 · 2018-03-13T14:27:02

5

We apply row reduction on the the matrix

# ((0,3,1),(1,1,2),(3,2,4))#

We first interchange #R_1# and #R_2# (this gives us a factor -1 in the final determinant)

# ((1,1,2),(0,3,1),(3,2,4))#

Then we carry out #R_3 larr R_3-3R_1 # (this does not change the determinant)

# ((1,1,2),(0,3,1),(0,-1,-2))#

Next do #R_3 larr R_3+1/3R_2# (again no change in the determinant)

# ((1,1,2),(0,3,1),(0,0,-5/3))#

The determinant of this triangular matrix is easily seen to be

#1 times 3 times (-5/3) = -5#

The original determinant was #(-1) times (-5) = 5#