Simple linear algebra problems. will rate quickly
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Simple linear algebra problems. will rate quickly

[From: ] [author: ] [Date: 11-10-13] [Hit: ]
Row reduce, if the right matrix can be turned into the identity matrix, then what is left on the right will be your inverse. If you cannot turn the right side of the matrix,......
If A=
1 -2 -9
0 1 1
0 0 1

then a^-1 =?


If A=
-3 3 10
3 -2 -6
-1 1 3

then a^-1 =?
A=
5 1 0 0
-11 -2 0 0
0 0 -1 -1
0 0 -4 -5

a^-1=?

i seem to be having some difficulties understanding matrix inversion could someone please help me? thank you so much

-
Set your matrix A to the identity matrix and row reduce, i.e.

[1 -2 -9| 1 0 0]
[0 1 1 | 0 1 0]
[0 0 1| 0 0 1]

Row reduce, if the right matrix can be turned into the identity matrix, then what is left on the right will be your inverse. If you cannot turn the right side of the matrix, then the matrix is invertible (you may want to check it with the determinant first as it is more efficient)

The row operations are

R₂ →R₂ - R₃
R₁ →R₁ + 9R₃
--------------------->
R₁ →R₁ + 2R₂

Your final matrix would be

[1 0 0| 1 2 7]
[0 1 0 | 0 1 -1]
[0 0 1| 0 0 1]

So your inverse is

[1 2 7]
[0 1 -1]
[0 0 1]

I let you do the other one

Yin
1
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