please answer the five questions clearly. I have provided the data. 7 Diagonal Matrices Diagonal Matrices...
Differention Equations - Can someone answer the checked numbers please? Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...
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)...
on matlab (1) Matrices are entered row-wise. Row commas. Enter 1 2 3 (2) Element A, of matrix A is accesser (3) Correcting an entry is easy to (4) Any submatrix of Ais obtained by d row wise. Rows are separated by semicolons and columns are separated by spaces ner A l 23:45 6. B and hit the return/enter kry matrix A is accessed as A Enter and hit the returnerter key an entry is easy through indesine Enter 19...
3. In the diagonal sum AEB:=A 0) 10 B) of two square matrices Amxm and Bnxn, each 0 represents a zero matrix of appropriate size. (i) Describe the size of each 0. (ii) describe the entries Crs of Ik 0e =: (Crs) (with ranges of r and s explicitly specified) in terms of 0 and the Kronecker delta symbol Sij which is defined as dij :=1 for i = j and di,j:= 0 for i 7 j.
even though DE These strange results actually pertain only to the special class of matrices known singular matrices, of which the matrices A, B, and C are examples. (Roughly, these matr ccs contain a row which is a multiple of another row.) Neverthcless, such examples d reveal the pitfalls of unwarranted extension of algcbraic theorems to matrix opcrations. ERCISE 4.5 Given A =-1 S 71. , and x-1X1 0-2 41,- 1. Calculate: (a) A (b A () ix (d) x...
Suppose A and B are matrices with matrix product AB. If bi, b2, ..., br are the columns of B, then Ab, Ab2, ..., Ab, are the columns of AB 1. Suppose A is an nxnmatrix such that A -SDS where D diag(di,d2,... dn) is a diagonal matrix, and S is an invertible matrix. Prove that the columns of S are eigenvectors of A with corresponding eigenvalues being the diagonal entries of D Before proving this, work through the following...
4.2 adding and multiplying matrices; using the summation sign 1.) A = , B = , C = , find: A + B b) C – A c) 3 A d) 4B + 2c 4.) Find the product matrices in the following (in each case, append beneath every matrix a dimension indicator): a.) [ ] c.)[ ] [ ] 6. Expand the following summation expressions: a.) c.)
(7) If possible, invert the following matrices 2 -2 1 211 B= 2 -3 -1 2-1 (8) A diagonal matrix A has all entries 0 except on the diagonal, that is, a 0 0 a2. 0 A= a nn Under which conditions is A nvertible and what is A-1?
6. For each of the following matrices A solve the eigenvalue problem. If A is diagonalizable, find a matrix P that diagonalizes A by a similarity transformation D-PlAP and the respective diagonal matrix D. If A is not diagonalizable, briefly explain why -1 4 2 (d) A-|-| 3 1 -1 2 2 -1 0 1 6 3 (a) A- (b)As|0 1 0| (c) A-1-3 0 11 -4 0 3
Note that is the -Jordan block of size m with 's in the diagonal and 1 to the right of the diagonal. 3. A Mercator matrix is a matrix A E Matn,n(R) such that pA(x) = (x-aj (x-4) for some α' E R, which are not necessarily distinct, such that 0 < α' < 2. Let Mn(R) be the set of Mercator matrices. As in Tutorial 1, if A EM(R) define the logarithm of A to be the matrix given...