Find a 2×22×2 matrix such that[−34−1−5][−3−14−5] ⎡⎣⎢⎢⎢⎢[ ⎤⎦⎥⎥⎥⎥] =[1001

If the matrix is invertible, find its inverse:A = .−1 2 −32 1 04 −2 5

Find the inverse of the matrix 𝐴 = [2 3 44 3 11 2 4] by using elementary rowtransformations.

Given matrix A use Gauss-Jordan elimination (with no row exchanges) to find A−1.

Find the inverse of the matrix A=[−1−11−1]

The 2×22×2 matrixA=(5−53−3)𝐴=(53−5−3)  has two distinct real eigenvalues.  1. Give the characteristic polynomial  for  A𝐴  in Maple notation in the form   t^2 + a*t + b          Characteristic polynomial  =       2. Find the set of eigenvalues for  A𝐴 . Enter your response in Maple set notation, i.e., enclosed in braces { } with the two eigenvalues separated by a comma. A typical answer might look like {-4, 7}.     The set of eigenvalues for  A𝐴 is       3. Find one eigenvector for each eigenvalue, using Maple notation for vectors, e.g.  <5, -6> for the vector  (5−6)(5−6)        An eigenvector for the smallest eigenvalue for  A𝐴 is            An eigenvector for the largest eigenvalue for  A𝐴 is