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Home > Matrix & Vector calculators > Division of two matrix example
3. Matrix Division example ( Enter your problem )
( Enter your problem )
  1. Definition and Examples
  2. Example-2
 		Other related methods
  1. Addition of two matrix
  2. Multiplication of two matrix
  3. Division of two matrix
  4. Power of a matrix
  5. Transpose of a matrix
  6. Determinant of a matrix
  7. Adjoint of a matrix
  8. Inverse of a matrix
  9. Prove that any two matrix expression is equal or not
  10. Minor of a matrix
  11. Cofactor of a matrix
  12. Trace of a matrix
1. Definition and Examples
(Previous example)		4. Power of a matrix
(Next method)

2. Example-2


2. Find A/B ...
A=[[2,3,1],[0,5,6],[1,1,2]],B=[[2,1,-1],[1,0,-1],[1,1,2]]

Solution:
|B| = 
 2  1  -1 
 1  0  -1 
 1  1  2 


 =
 2 × 
 0  -1 
 1  2 
 -1 × 
 1  -1 
 1  2 
 -1 × 
 1  0 
 1  1 


=2 xx (0 × 2 - (-1) × 1) -1 xx (1 × 2 - (-1) × 1) -1 xx (1 × 1 - 0 × 1)

=2 xx (0 +1) -1 xx (2 +1) -1 xx (1 +0)

=2 xx (1) -1 xx (3) -1 xx (1)

= 2 -3 -1

=-2


Adj(B) = 
Adj
21-1
10-1
112


 = 
 + 
 0  -1 
 1  2 
 - 
 1  -1 
 1  2 
 + 
 1  0 
 1  1 
 - 
 1  -1 
 1  2 
 + 
 2  -1 
 1  2 
 - 
 2  1 
 1  1 
 + 
 1  -1 
 0  -1 
 - 
 2  -1 
 1  -1 
 + 
 2  1 
 1  0 
T


 = 
+(0 × 2 - (-1) × 1)-(1 × 2 - (-1) × 1)+(1 × 1 - 0 × 1)
-(1 × 2 - (-1) × 1)+(2 × 2 - (-1) × 1)-(2 × 1 - 1 × 1)
+(1 × (-1) - (-1) × 0)-(2 × (-1) - (-1) × 1)+(2 × 0 - 1 × 1)
T


 = 
+(0 +1)-(2 +1)+(1 +0)
-(2 +1)+(4 +1)-(2 -1)
+(-1 +0)-(-2 +1)+(0 -1)
T


 = 
1-31
-35-1
-11-1
T


 = 
1-3-1
-351
1-1-1


"Now, "B^(-1)=1/|B| × Adj(B)

 = 1/(-2) ×
1-3-1
-351
1-1-1


 = 
-0.51.50.5
1.5-2.5-0.5
-0.50.50.5


A×(B^(-1))=
231
056
112
×
-0.51.50.5
1.5-2.5-0.5
-0.50.50.5


=
2×-0.5+3×1.5+1×-0.52×1.5+3×-2.5+1×0.52×0.5+3×-0.5+1×0.5
0×-0.5+5×1.5+6×-0.50×1.5+5×-2.5+6×0.50×0.5+5×-0.5+6×0.5
1×-0.5+1×1.5+2×-0.51×1.5+1×-2.5+2×0.51×0.5+1×-0.5+2×0.5


=
-1+4.5-0.53-7.5+0.51-1.5+0.5
0+7.5-30-12.5+30-2.5+3
-0.5+1.5-11.5-2.5+10.5-0.5+1


=
3-40
4.5-9.50.5
001


This material is intended as a summary. Use your textbook for detail explanation.
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1. Definition and Examples
(Previous example)		4. Power of a matrix
(Next method)


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