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1. Find Inverse of matrix A
A =
OR A =
 

2. Solve Simultaneous Equations
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SolutionHelp1.1 Inverse1.2 Inverse Guess Elimination2.1 Inverse Matrix2.2 Cramer's Rule2.3 Gauss Elimination2.4 Gauss Sield
1. Find Inverse of a matrix
1. Find Inverse of matrix

`| A |=|[1,2,3],[0,1,0],[2,3,1]|`

` = 1 (1 × 1 - 0 × 3) - 2 (0 × 1 - 0 × 2) + 3 (0 × 3 - 1 × 2)`

` = 1 (1 - 0) - 2 (0 - 0) + 3 (0 - 2)`

` = 1 (1) - 2 (0) + 3 (-2)`

` = 1 - 0 - 6`

` = -5`


`Adj(A)=Adj[[1,2,3],[0,1,0],[2,3,1]]`

`=[[+(1 × 1 - 0 × 3),-(0 × 1 - 0 × 2),+(0 × 3 - 1 × 2)],[-(2 × 1 - 3 × 3),+(1 × 1 - 3 × 2),-(1 × 3 - 2 × 2)],[+(2 × 0 - 3 × 1),-(1 × 0 - 3 × 0),+(1 × 1 - 2 × 0)]]^T`

`=[[1,0,-2],[7,-5,1],[-3,0,1]]^T`

`=[[1,7,-3],[0,-5,0],[-2,1,1]]`


`"Now, "A^(-1) = 1/| A | × Adj(A)`

`=1/-5 × [[1,7,-3],[0,-5,0],[-2,1,1]]`

`=[[-1/5,-7/5,3/5],[0,1,0],[2/5,-1/5,-1/5]]`

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