Find the non-singular matrices `A ,`
if its is given that `a d j(A)=[[-1,-2, 1],[ 3 ,0,-3],[ 1,-4, 1]]`
Text Solution
AI Generated Solution
To find the non-singular matrix \( A \) given that \( \text{adj}(A) = \begin{bmatrix} -1 & -2 & 1 \\ 3 & 0 & -3 \\ 1 & -4 & 1 \end{bmatrix} \), we will follow these steps:
### Step 1: Determine the order of the matrix
Since \( \text{adj}(A) \) is a \( 3 \times 3 \) matrix, the order \( n \) of matrix \( A \) is 3.
### Step 2: Use the property of determinants
We use the property that:
\[
...
Topper's Solved these Questions
ADJOINTS AND INVERSE OF MATRIX
RD SHARMA|Exercise QUESTION|1 Videos
ALGEBRA OF MATRICES
RD SHARMA|Exercise Solved Examples And Exercises|410 Videos
Similar Questions
Explore conceptually related problems
Find the non-singular matrices A, if it is given that adj(A)=[-1-2130-31-41]
If A and B are non - singular matrices of order three such that adj(AB)=[(1,1,1),(1,alpha, 1),(1,1,alpha)] and |B^(2)adjA|=alpha^(2)+3alpha-8 , then the value of alpha is equal to
Prove that the inverse of [[A,O],[B,C]] is [[A^(-1),O],[-C^(-1)BA^(-1),C^(-1)]] , where A, Care non-singular matrices and O is null matrix and find the inverse. [[1,0,0,0],[1,1,0,0],[1,1,1,0],[1,1,1,1]]
If A and adj A are non-singular square matrices of order n, then adj (A^(-1))=
Find the inverse of each of the matrices (if it exists) given in [{:(-1,5),(-3,2):}]
A square non-singular matrix A satisfies A^2-A+2I=0," then "A^(-1) =
Compute the adjoint of each of the following matrices: [[1, 2, 2],[ 2 ,1 ,2],[ 2, 2, 1]] (ii) [[1, 2, 5],[ 2, 3,1],[-1, 1, 1]] (iii) [[2,-1, 3],[ 4, 2, 5],[ 0, 4,-1]] (iv) [[2, 0,-1],[ 5, 1, 0],[ 1, 1, 3]] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.
Find the matrices A and B such that A+B=[[1,0,2] , [2,2,2] , [1,1,2]] and A-B=[[1,4,4] , [4,3,0] , [-1,-1,2]]
Are the following matrices non-singular ? A=[[1,2,3],[2,4,6],[1,4,5]] , B=[[1,2,3],[2,4,6],[3,5,9]]
