Linear Algebra with MapleV homework3



Email: lbg@kowon.dongseo.ac.kr


For a randomly generated 5x5 matrix A, verify the following identity.

  1. A adj(A) = adj(A) A = det(A) I
  2. adj(A)^t = adj(A^t)
  3. det(A) = det(A^t)
  4. the matrix B obtained by interchanging the first two rows of A satisfies det(B) = -det(A)
  5. any matrix obtained by adding a multiple of the first row to the second has the same determinant
  6. multiplying the first row by a scalar k changes the determinant by a mutiple of k




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