Determine those values of λ for which the matrix   1 λ 0 3 2 0 1 2 1   is not invertible

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

If [ ] then find the eigen values for the matrix

Let λk, k = 1, 2, ..., n, be the eigenvalues of an n × n invertible matrix A.(a) (2 pts) Show that λk 6 = 0, k = 1, 2, ..., n.(b) (8 pts) Show that the eigenvalues of A−1 are 1λk, k = 1, 2, ..., n

To find the eigenvalues, computedet3 − λ 0 0−3 4 − λ 90 0 3 − λ = (3 − λ)(4 − λ)(3 − λ).So the eigenvalues are λ = 3 and λ = 4.We can find two linearly independent eigenvectors301 ,130 corresponding to the eigenvalue 3, and oneeigenvector010 with eigenvalue 4. The diagonalized form of the matrix is3 0 0−3 4 90 0 3 =3 1 00 3 11 0 03 0 00 3 00 0 40 0 11 0 −3−3 1 9 .Note that if you chose different eigenvectors, your matrices will be different. The middle matrix should haveentries 3, 3, 4 in some order, and you should multiply out the product to make sure you have the right answer.

A square matrix A is invertible if and only ifQuestion 9Select one: 𝜆 = 1 𝑖𝑠 𝑎𝑛 𝑒𝑖𝑔𝑒𝑛𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴.𝜆 = 0 𝑖𝑠 𝑎𝑛 𝑒𝑖𝑔𝑒𝑛𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴. 𝜆 = 0 𝑖𝑠 𝑛𝑜𝑡 𝑎𝑛 𝑒𝑖𝑔𝑒𝑛𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴.𝜆 = 1 𝑖𝑠 𝑛𝑜𝑡 𝑎𝑛 𝑒𝑖𝑔𝑒𝑛𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴.