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Find the adjoint of the matrix A=[(1,1,1...

Find the adjoint of the matrix `A=[(1,1,1),(2,1,-3),(-1,2,3)]`.

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To find the adjoint of the matrix \( A = \begin{pmatrix} 1 & 1 & 1 \\ 2 & 1 & -3 \\ -1 & 2 & 3 \end{pmatrix} \), we will follow these steps: ### Step 1: Find the Cofactor Matrix The cofactor \( C_{ij} \) of an element \( a_{ij} \) in matrix \( A \) is calculated using the formula: \[ C_{ij} = (-1)^{i+j} \cdot M_{ij} \] ...
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CENGAGE ENGLISH-MATRICES-ILLUSTRATION
  1. If abc=p and A=[(a,b,c),(c,a,b),(b,c,a)], prove that A is orthogonal i...

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  2. Let A be an orthogonal matrix, and B is a matrix such that AB=BA, then...

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  3. Find the adjoint of the matrix A=[(1,1,1),(2,1,-3),(-1,2,3)].

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  4. If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(...

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  5. If A is a square matrix such that A(adjA)=[(4,0,0),(0,4,0),(0,0,4)], t...

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  6. Let A be a square matrix of order 3 such that adj. (adj. (adj. A)) =...

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  7. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

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  8. Matrices a and B satisfy AB=B^(-1), where B=[(2,-1),(2,0)]. Find (i...

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  9. Given the matrices A and B as A=[(1,-1),(4,-1)] and B=[(1,-1),(2,-2)]....

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  10. If M is the matrix [(1,-3),(-1,1)] then find matrix sum(r=0)^(oo) ((-1...

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  11. Let p be a non singular matrix, and I + P + p^2 + ... + p^n = 0, then ...

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  12. If A and B are square matrices of same order such that AB=O and B ne O...

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  13. If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsi...

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  14. If the matrices, A, B and (A+B) are non-singular, then prove that [A(A...

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  15. If matrix a satisfies the equation A^(2)=A^(-1), then prove that A^(2^...

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  16. If A and B are non-singular symmetric matrices such that AB=BA, then p...

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  17. If A is a matrix of order n such that A^(T)A=I and X is any matric suc...

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  18. Show that two matrices A=[(1,-1,0),(2,1,1)] and B=[(3,0,1),(0,3,1)] ...

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  19. Using elementary transformations, find the inverse of the matrix : ...

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  20. Let a be a 3xx3 matric such that [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),...

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