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If Delta=|[a(11), a(12 ), a(13)], [a(21...

If `Delta=|[a_(11), a_(12 ), a_(13)], [a_(21), a_(22), a_(23)],[ a_(31) , a_(32), a_(33)]|` and `A_(i j)` is cofactors of `a_(ij)`, then value of `Delta` is given by
i) `a_(11) A_(31)+a_(12) A_(32)+a_(13) A_(33)`
ii) `a_(11) A_(11)+a_(12) A_(21)+a_(13) A_(31)`
iii) `a_(21) A_(11)+a_(22) A_(12)+a_(23) A_(13)`
iv) `a_(11) A_(11)+a_(21) A_(21)+a_(31) A_(31)`

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V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Using cofactors of element of second row evaluate Delta=|[5, 3, 8],[...

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  2. Using co-factors of elements of third column, evaluate Delta=|[1, x,...

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  3. If Delta=|[a(11), a(12 ), a(13)], [a(21), a(22), a(23)],[ a(31) , a...

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  4. If A=[[2, 3],[ 1, -4]] and B=[[1, -2],[ -1, 3]], then verify tha...

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  5. Show that the matrix A=[[2, 3],[ 1, 2]] Satisfies the equation A^2-...

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  6. Find the adjoint of each of the matrices [[1 , 2],[ 3, 4]]

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  7. Find the adjoint of the matrix [[1 , -1, 2],[ 2, 3, 5],[ -2, 0, ...

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  8. Verify A (adj A)=(adj A)A=|A|I in the following matrices. [[2,3],[-4,-...

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  9. Find the inverse of the following matrics. [[2,-2],[4,3]]

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  10. Find the inverse of the following matrics. [[-1,5],[-3,2]]

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  11. Find the inverse of each of the matrices [[1, 2, 3],[ 0, 2, 4],[...

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  12. Find the inverse of the following A=[[1,0,0],[3,3,0],[5,2,-1]]

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  13. Find the inverse of each of the matrices [[2 , 1 , 3],[ 4, -1, 0],[...

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  14. Find the inverse of the following A=[[1,-1,2],[0,2,-3],[3,-2,4]]

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  15. Find the inverse of each of the matrices. [[1, 0, 0],[ 0 , cos alph...

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  16. Let A=[[3 , 7],[ 2, 5]] and B=[[6 , 8],[ 7, 9]] Verify that (A B)...

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  17. If A =[[3,1],[-1,2]],show that A^2-5A + 7I=0 Hence, find A^(-1)

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  18. For the matrix A=[[3,2],[1,1]],find the numbers a and b such that A^2+...

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  19. For the matrix A=[[1,1,1],[1,2,-3],[2,-1,3]] show that A^3-6A^2+5A+11I...

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  20. Let A be a non-singular square matrix of order 3xx3.Then |adj A| is .....

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