Find the inverse of each of the following matrices. begin{bmatrix}1 & 0&1-1&1&1 -1&-2&-3 end{bmatrix}

postillan4 2020-12-05 Answered
Find the inverse of each of the following matrices.
[101111123]
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Expert Answer

Nathalie Redfern
Answered 2020-12-06 Author has 99 answers
Step 1
Given matrix is
A=[101111123]
firstly, we will find all cofactors by using the formula
Aij=(1)i+jMij
where Mij are minors.
A11=(1)1+1(3+2)=1
A12=(1)1+2(3+1)=4
A13=(1)1+3(2+1)=3
A21=(1)2+1(0+2)=2
A22=(1)2+2(3+1)=2
A23=(1)2+3(2+0)=2
A31=(1)3+1(01)=1
A32=(1)3+2(1+1)=2
A33=(1)3+3(1+0)=1
Now, Adjoint A matrix is transpose of cofactors matrix.
AdjA=[143222121]T=[121422321]
Step 2
Now, we ill evaluate the determinant of matrix A
|A|=a11A11+a12A12+a13A13
=1(1)+0(4)+1(3)=2
Since, determinant of A is non-zero, therefore, inverse matrix of A exists and is obtained as
A1=1|A|AdjA
A1=12[121422321]
Step 3
Ans:
A1=12[121422321]
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Jeffrey Jordon
Answered 2022-01-27 Author has 2087 answers

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