Home > Matrix & Vector calculators > Inverse of matrix using Adjoint method example

1. Adjoint method example ( Enter your problem )
  1. Example [311-121111]
  2. Example [231056112]
  3. Example [23410]
  4. Example [5142]
Other related methods
  1. Adjoint method
  2. Gauss-Jordan Elimination method
  3. Cayley Hamilton method

2. Example [231056112]
(Next example)

1. Example [311-121111]





1. Find Inverse of matrix
A=[311-121111]


Solution:
|A| = 
 3  1  1 
 -1  2  1 
 1  1  1 


 =
 3 × 
 2  1 
 1  1 
 -1 × 
 -1  1 
 1  1 
 +1 × 
 -1  2 
 1  1 


=3×(2×1-1×1)-1×(-1×1-1×1)+1×(-1×1-2×1)

=3×(2-1)-1×(-1-1)+1×(-1-2)

=3×(1)--1×(-2)+1×(-3)

=3+2-3

=2


Adj(A) = 
Adj
311
-121
111


 = 
 + 
 2  1 
 1  1 
 - 
 -1  1 
 1  1 
 + 
 -1  2 
 1  1 
 - 
 1  1 
 1  1 
 + 
 3  1 
 1  1 
 - 
 3  1 
 1  1 
 + 
 1  1 
 2  1 
 - 
 3  1 
 -1  1 
 + 
 3  1 
 -1  2 
T


 = 
+(2×1-1×1)-(-1×1-1×1)+(-1×1-2×1)
-(1×1-1×1)+(3×1-1×1)-(3×1-1×1)
+(1×1-1×2)-(3×1-1×(-1))+(3×2-1×(-1))
T


 = 
+(2-1)-(-1-1)+(-1-2)
-(1-1)+(3-1)-(3-1)
+(1-2)-(3+1)+(6+1)
T


 = 
12-3
02-2
-1-47
T


 = 
10-1
22-4
-3-27


Now, A-1=1|A|×Adj(A)

 = 12 ×
10-1
22-4
-3-27


 = 
120-12
11-2
-32-172



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2. Example [231056112]
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