example 3 inverse of a 3 x 3 matrix chapter 7.4 find the inverse of. 2009 pblpathways
TRANSCRIPT
example 3 Inverse of a 3 x 3 Matrix
Chapter 7.4
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2009 PBLPathways
2009 PBLPathways
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2009 PBLPathways
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2 1 2 1 0 0
1 0 1 0 1 0
4 2 3 0 0 1
R1 R11 0 1 0 1 0
2 1 2 1 0 0
4 2 3 0 0 1
2R1 + R2 R21 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
2 0 2 0 2 0
2 1 2 1 0 0
0 1 0 1 2 0
2009 PBLPathways
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2 1 2 1 0 0
1 0 1 0 1 0
4 2 3 0 0 1
R1 R21 0 1 0 1 0
2 1 2 1 0 0
4 2 3 0 0 1
2R1 + R2 R21 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
2 0 2 0 2 0
2 1 2 1 0 0
0 1 0 1 2 0
2009 PBLPathways
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2 1 2 1 0 0
1 0 1 0 1 0
4 2 3 0 0 1
R1 R21 0 1 0 1 0
2 1 2 1 0 0
4 2 3 0 0 1
2R1 + R2 R21 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
2 0 2 0 2 0
2 1 2 1 0 0
0 1 0 1 2 0
2009 PBLPathways
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2 1 2 1 0 0
1 0 1 0 1 0
4 2 3 0 0 1
R1 R21 0 1 0 1 0
2 1 2 1 0 0
4 2 3 0 0 1
2R1 + R2 R21 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
2 0 2 0 2 0
2 1 2 1 0 0
0 1 0 1 2 0
2009 PBLPathways
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2 1 2 1 0 0
1 0 1 0 1 0
4 2 3 0 0 1
R1 R21 0 1 0 1 0
2 1 2 1 0 0
4 2 3 0 0 1
2R1 + R2 R21 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
2 0 2 0 2 0
2 1 2 1 0 0
0 1 0 1 2 0
2009 PBLPathways
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2 1 2 1 0 0
1 0 1 0 1 0
4 2 3 0 0 1
R1 R21 0 1 0 1 0
2 1 2 1 0 0
4 2 3 0 0 1
2R1 + R2 R21 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
2 0 2 0 2 0
2 1 2 1 0 0
0 1 0 1 2 0
2009 PBLPathways
Find the inverse of .
2 1 2
1 0 1
4 2 3
A
2 1 2 1 0 0
1 0 1 0 1 0
4 2 3 0 0 1
R1 R21 0 1 0 1 0
2 1 2 1 0 0
4 2 3 0 0 1
2R1 + R2 R21 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
2 0 2 0 2 0
2 1 2 1 0 0
0 1 0 1 2 0
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 1 0 1 0
0 1 0 1 2 0
0 2 1 0 4 1
-4R1 + R3 R3
4 0 4 0 4 0
4 2 3 0 0 1
0 2 1 0 4 1
1 0 1 0 1 0
0 1 0 1 2 0
4 2 3 0 0 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
2R2 + R3 R3
0 2 0 2 4 0
0 2 1 0 4 1
0 0 1 2 0 1
2009 PBLPathways
1 0 0 2 1 1
0 1 0 1 2 0
0 0 1 2 0 1
R3 + R1 R1
0 0 1 2 0 1
1 0 1 0 1 0
1 0 0 2 1 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
1
2 1 1
1 2 0
2 0 1
A
2009 PBLPathways
1 0 0 2 1 1
0 1 0 1 2 0
0 0 1 2 0 1
R3 + R1 R1
0 0 1 2 0 1
1 0 1 0 1 0
1 0 0 2 1 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
1
2 1 1
1 2 0
2 0 1
A
2009 PBLPathways
1 0 0 2 1 1
0 1 0 1 2 0
0 0 1 2 0 1
R3 + R1 R1
0 0 1 2 0 1
1 0 1 0 1 0
1 0 0 2 1 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
1
2 1 1
1 2 0
2 0 1
A
2009 PBLPathways
1 0 0 2 1 1
0 1 0 1 2 0
0 0 1 2 0 1
R3 + R1 R1
0 0 1 2 0 1
1 0 1 0 1 0
1 0 0 2 1 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
1
2 1 1
1 2 0
2 0 1
A
2009 PBLPathways
1 0 0 2 1 1
0 1 0 1 2 0
0 0 1 2 0 1
R3 + R1 R1
0 0 1 2 0 1
1 0 1 0 1 0
1 0 0 2 1 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
1
2 1 1
1 2 0
2 0 1
A
2009 PBLPathways
1 0 0 2 1 1
0 1 0 1 2 0
0 0 1 2 0 1
R3 + R1 R1
0 0 1 2 0 1
1 0 1 0 1 0
1 0 0 2 1 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
1
2 1 1
1 2 0
2 0 1
A
2009 PBLPathways
1 0 0 2 1 1
0 1 0 1 2 0
0 0 1 2 0 1
R3 + R1 R1
0 0 1 2 0 1
1 0 1 0 1 0
1 0 0 2 1 1
1 0 1 0 1 0
0 1 0 1 2 0
0 0 1 2 0 1
1
2 1 1
1 2 0
2 0 1
A