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**[SOLVED] Finding inverse of a matrix and solving given equations.**

Hi,

I have a quiz tomorrow and I am looking at the sample quiz right now but I don't understand how the answers work!

Here is the question:

Find the inverse of the matrix A=

-1 3 3

-2 1 2

0 1 1

Hence solve the following systems of equations:

-x1 + 3x2 + 3x3 = 5

-2x1 + x2 + 2x3 = 2

x2 + x3 = 1

and

-x + 3z = -5

2x - y - 4z = 2

-2x + y + 5z = -1

The answer says the inverse of A

-1 0 3

2 -1 -4

-2 1 5

Then it spells out how to solve the equations but the is the part that confuses me:

"The first system of equations corresponds to the matrix equation A

[x1 = [5

x2 = 2

x3 ] = 1]

Therefore, as A is invertible (i.e. A-1 exists),

[x1

x2

x3]

=A inverse of

[5

2

1]

which =

[-1 0 3 [5 [-2

2 -1 -4 2 = 4

-2 1 5 ] 1] -3 ]

So x1 = -2, x2 = 4, x3 = -3.

Can someone please explain how they just did that because I really can't understand where they derive -2, 4 , 3 from and what they do with [5, 2 ,1]

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