(7) If possible, invert the following matrices 2 -2 1 211 B= 2 -3 -1 2-1...
please answer the five questions clearly. I have provided the data. 7 Diagonal Matrices Diagonal Matrices If A = (a) is a square matrix, then the entries and are called diagonal entries. A square matrix is called diagonal if all non-diagonal entries are zeros. Explore what happens if we add, subtract or multiply diagonal matrices. A and B are the same matrices in previous sections ( section 5.) Type D-diag(diag(A)) to create a diagonal matrix from A. Type E-diag(diag(B)) to...
16. Diagonalize the following matrices if possible. (If not possible explain why not) Then compute A2. (Use the diagonal matrix to do the computation if A was diagonalizable) One of the Eigen-values is provided to get you started. A= [-2 3 1-9 10 -1 15 4 -2 10. 2=4
3) (9 points) For each of the following matrices Find the eigenvalues and associated eigenvectors. If possible, state the matrices P and D, such that A = PDP-1. (Hint: P is a matrix containing eigenvectors of A on its columns, and D is a diagonal matrix.) If it is not possible to find P and D, just state so. 11-133b a. A = 1 2 2 1-2 -2 -2 2 0 -1 3] b. A = [1 -4 110 0...
Use the following matrices to perform the indicated operation, when possible. (If not possible, enter IMPOSSIBLE into any cell of the matrix.) B = 1 1 7 0 E = 2 0 4 8 3 2 1 7 2 0 7 1 0 2 FIND EB.
4 Consider the following nonsingular matrix P = a) Find P by hand. by hand. b) Use P and P-1 to find a matrix B that is similar to A c) Notice that A is a diagonal matrix (a matrix whose entries everywhere besides the main diagonal are 0). As you may recall from #5 on Lab 2, one of the many nice properties of diagonal matrices (of order n) is that 0 1k 0 a11 0 0 a11 0...
15. Use the characteristic equation to find the real eigenvalues of the following matrices. (a) [ ] 6 (b) | 9 -9 -6 -9 6 -6 3 1 16. Diagonalize the following matrices if possible. (If not possible explain why not)Then compute A2. (Use the diagonal matrix to do the computation if A was diagonalizable) One of the Eigen-values is provided to get you started. A= 10 -1 15 3 -9 2=4 -2 10)
1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2 1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2
8 and 11 Will h x n lower triangular matrices. Show it's a w It's a 8. Dan will represent the set of all n x n diagonal matrices. Show it's a subspace of Mr. 9. For a square matrix AE M , define the trace of A, written tr(A) to be the sum of the diagonal entries of A (i.e. if A= a) then tr(A) = 211 + a2 + ... + ann). Show that the following subset of...
I. Consider the set of all 2 × 2 diagonal matrices: D2 under ordinary matrix addition and scalar multiplication. a. Prove that D2 is a vector space under these two operations b. Consider the set of all n × n diagonal matrices: di 00 0 d20 0 0d under ordinary matrix addition and scalar multiplication. Generalize your proof and nota in (a) to show that D is a vector space under these two operations for anyn I. Consider the set...
1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а) А — 1 0 1 -1 1 0 2 -2 (Ъ) А %— -2 -2 -4 -2 2 |3 0 7 0 5 0 7 0 3 (с) А %— 1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а)...