SOLUTION: Find the inverse of the matrix if it exists. A= [3,-1,0] [4,1,0] [0,0,4] A^-1=

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Question 626896: Find the inverse of the matrix if it exists.
A=
[3,-1,0]
[4,1,0]
[0,0,4]
A^-1=
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

A=%28matrix%283%2C3%2Ca1%2Cb1%2Cc1%2Ca2%2Cb2%2Cc2%2Ca3%2Cb3%2Cc3%29%29 =%28matrix%283%2C3%2C3%2C-1%2C0%2C4%2C1%2C0%2C0%2C0%2C4%29%29

I. find value of determinant =  a1(b2c3-c2b3) - b1(a2c3-c2a3) + c1(a2b3-b2a3) = 28

II. Then Apply formula for the Inverse:

A%5E%28-1%29 = 1/d



A%5E%28-1%29  = 1/28%28matrix%283%2C3%2C4%2C4%2C0%2C-16%2C12%2C0%2C0%2C0%2C7%29%29