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
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 -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