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AP EAMCET202120 Aug 2021Evening ShiftMathematicsMatricesActual

Let A be a n × n matrix such that A is upper-triangular. Then adj A =

Options

  1. Alower triangular matrix
  2. Bupper triangular matrix
  3. Cdiagonal matrix
  4. Dscalar matrix

Correct answer

B. upper triangular matrix

Step-by-step solution

Let, A n × n   = a 11 a 12 a 13 . . . . . . . . a 1 n 0 a 22 a 23 . . . . . . a 2 n 0 0 a 33 . . . . . . . . a 3 n . . . . . . . . . . . . . . . . . . . . . . 0 0 0 a n n Cofactors of all the elements of upper triangle are zero. adj A = A 11 0 0 . . . . . . . . 0 A 12 A 22 0 . . . . . . 0 A 13 A 23 A 33   . . . . . . . . 0 . . . . . . . . . . . . . . . . . . . . . . A 1 n A 2 n . . . . . A n n T adj A = A 11 A 12 A 13 . . . . . . . . A 1 n 0 A 22 A 23 . . . . . . A 2 n 0 0 A 33 . . . . . . . . A 3 n

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