Known Matrix:"A=\\begin{bmatrix}\n 2 & 1 & 2 \\\\\n 1 & 2 & 2 \\\\\n 1 & 1 & 3\n\\end{bmatrix}""B=\\begin{bmatrix}\n 3 & 0 & 2 \\\\\n 0 & 1 & a \\\\\n 0 & 2 & 2a\n\\end{bmatrix}"Determine the characteristic equation det(A − λI) = 0 of the matrix aboveDetermine the eigenvalues of the matrix and the basis of the eigenspaceNote: In matrix B, let the value of a be so that the eigenvalues and the basis of the eigenspace are dependent on a.