(10 points) Given a square matrix A = (aij) j=1, let us define its Gershgorin disks...

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(10 points) Given a square matrix A = (aij) j=1, let us define its Gershgorin disks for i = 1, n by: " D = Di = { = C |= n z = C: zai lal j=1,ji These are disks in the complex plane C, which are centered at the diagonal entries ai, and whose radius is the sum of the absolute values of the off-diagonal entries in the i-th row. (1). Draw a picture (on the same plane) of the Gershgorin disks D, D2, D3 for the matrix 2 1 1 A = = 1 2 1 1 2 3 (2). Without computing the eigenvalues of the matrix, tell whether the matrix given in part (1) could have an eigenvalue greater than 6, or less than zero, based on your picture. (10 points) Given a square matrix A = (aij) j=1, let us define its Gershgorin disks for i = 1, n by: " D = Di = { = C |= n z = C: zai lal j=1,ji These are disks in the complex plane C, which are centered at the diagonal entries ai, and whose radius is the sum of the absolute values of the off-diagonal entries in the i-th row. (1). Draw a picture (on the same plane) of the Gershgorin disks D, D2, D3 for the matrix 2 1 1 A = = 1 2 1 1 2 3 (2). Without computing the eigenvalues of the matrix, tell whether the matrix given in part (1) could have an eigenvalue greater than 6, or less than zero, based on your picture.