Find the determinant of this 4x4 matrix, but by reducing it to rowechelon form [

Question

Find the determinant of this 4x4 matrix, but by reducing it to rowechelon form
[ 2 3 1 -4 ] [5 6 2 4 ] [1 2 1 1 ] [-3 2 6 5 ]
Determinants are easy, but I just can't understand rowechelon. A thorough explanation of steps would beappreciated. I have several probelms just like this one todo.
[ 2 3 1 -4 ] [5 6 2 4 ] [1 2 1 1 ] [-3 2 6 5 ]
Determinants are easy, but I just can't understand rowechelon. A thorough explanation of steps would beappreciated. I have several probelms just like this one todo.

Explanation / Answer

A= 2 3 1.0 -4.0 5 6 2.0 4.0 1 2 1.0 1.0 -3 2 6.0 5.0 NR2=R2-5R1/2…NR3=R3-R1/2…NR4=R4+3R1/2 2.000 3.000 1.000 -4.000 0.000 -1.500 -0.500 14.000 0.000 0.500 0.500 3.000 0.000 6.500 7.500 -1.000 NR3=R3+R2/3….NR4=R4+13R2/3 2 3 1 -4 0 -1.5 -0.5 14 0 0 0.333333333 7.666666667 0 0 5.333333333 59.66666667 NR4=R4-16R3 2 3 1 -4 0 -1.5 -0.5 14 0 0 0.333333333 7.666666667 0 0 0 -63 HENCE |A| = 2(-1.5)(1/3)(-63) = 63

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