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Find the inverse of the matrix A = {:[(a...

Find the inverse of the matrix `A = {:[(a,b),(c,(1+bc)/a)]` and show that : `aA^-1 = (a^2+bc+1)I-aA`

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Using Cofactors of elements of third column, evaluate triangle - |[1,x...

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  2. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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  3. Find the inverse of the matrix A = {:[(a,b),(c,(1+bc)/a)] and show tha...

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  4. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

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  5. If A = [[2,-3,5],[3,2,-4],[1,1,-2]] find A^-1. Using A^-1 solve the s...

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  6. Let P = [[3, -1, -2],[2 ,0 ,alpha ],[3, -5, 0]], where alpha in R. Sup...

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  7. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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  8. Let M and n be two 3xx3 matrices such that MN = NM. Further, If Mne ...

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  9. For 3xx3 martrices M and N, which of the following statement (s) is ...

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  10. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

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  11. If A is a matrix of order mxx m such that A^(2) +A + 2I = O, then

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  12. Let a, b, and c be three real numbers satisfying [(a,b,c)][[1,9,7],[...

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  13. Let omega be a solution of z^3-1 = 0 If a = 2 , b=8 and c =7 then the ...

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  14. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  15. A complex number U = 4+2i.The value of |U| is

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  16. Let A be the set of all 3× 3 symmetric matrices all of whose either 0 ...

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  17. Let A be the set of all 3xx3 symmetric matrices all of whoes entries...

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  18. For a 2xx2 matrix, A = [a(ij)], whose elements are given by a(ij) = ...

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  19. If A is a square matrix such that A^2 = A, then write the value of (I+...

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  20. Evaluate the following determinants: {:|(3,x),(x,1)| = |(3,2),(4,1)|

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