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Find adjoint of the matrice in[(1,-1, 2)...

Find adjoint of the matrice in`[(1,-1, 2),( 2, 3, 5),(-2, 0, 1)]`

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To find the adjoint of the matrix \( A = \begin{pmatrix} 1 & -1 & 2 \\ 2 & 3 & 5 \\ -2 & 0 & 1 \end{pmatrix} \), we will follow these steps: ### Step 1: Find the Cofactor Matrix The adjoint of a matrix is the transpose of its cofactor matrix. We will first calculate the cofactors for each element of the matrix. The cofactor \( C_{ij} \) of an element \( a_{ij} \) is given by: \[ C_{ij} = (-1)^{i+j} \cdot M_{ij} ...
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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Find the inverse the matrix (if it exists) given in[(2, 1, 3),( 4,-1, ...

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  2. If A=((2,-3,5),(3,2,-4),(1,1,-2)) find A^(-1). Use it to solve the sys...

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  3. Find adjoint of the matrice in[(1,-1, 2),( 2, 3, 5),(-2, 0, 1)]

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  4. Verify A (a d j A) = (a d j A) A = |A|I for [(2 ,3),(-4,-6)]

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  5. Find adjoint of the matrice in[(1, 2),( 3, 4)]

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  6. Find the inverse the matrix (if it exists)given in[(-1, 5),(-3, 2)]

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  7. Find the inverse the matrix (if it exists)given in[(1, 2, 3),( 0, 2, 4...

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  8. Verify A (a d j A) = (a d j A) A = |A|I [(1,-1,2),(3,0,-2),(1,0,3)]

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  9. Find the inverse the matrix (if it exists)given in[(2,-2),( 4, 3)]

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  10. Evaluate |(x, y, x+y),( y, x+y, x),( x+y, x, y)|.

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  11. Solve system of linear equations, using matrix method, 5x + 2y = 3" "...

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  12. Without expanding the determinant, prove that |(a,a^2,bc),(b,b^2,ca),(...

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  13. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

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  14. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

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  15. Solve the equation |(x+a, x,x),(x,x+a, x),(x,x,x+a)|=0, a!= 0

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  16. Prove: |a^2b c a c+c^2a^2+a bb^2a c a bb^2+b cc^2|=4a^2b^2c^2

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  17. Solve system of linear equations, using matrix method, 2x+y+z=1" "x-2...

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  18. Solve system of linear equations, using matrix method, x - y + z = 4"...

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  19. The sum of three numbers is 6. If multiply theird number by 3 and add ...

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  20. Solve the following system of equations by matrix method. 3x-2y + 3z=...

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