How do you find the inverse of #A=##((9, 6, 12), (6, 4, 8), (12, 8, 16)) #?

1 Answer
Feb 13, 2016

Answer:

This matrix has no inverse since its determinant is zero.

Explanation:

Notice that the third row is twice the second row, so these rows are not linearly independent. So there can be no inverse.

Still need convincing?

#abs((9,6,12),(6,4,8),(12,8,16))#

#=9 abs((4,8),(8,16)) + 6 abs((8,6),(16,12)) + 12 abs((6,4),(12,8))#

#=9 (4*16-8*8) + 6(8*12-6*16) + 12(6*8-4*12)#

#=0+0+0 = 0#