Let Tn = (tij) denote the nxn matrix such that for each index i, tji = a and tij = b for j not = to i. Verify that Tn = (a-b)In + bEn where En is the nxn matrix of all 1's. Find the determinate and the eigenvalues of Tn.
A certain 4x4 real matrix is known to have these properties: 1) Two of the eigenvalues of A are L1= 3 and L2= 2. 2) The number 3 is an eigenvalue of the matrix A + 2I. 3) det. A = 12. What are the other 2 eigenvalues of A and what is the characteristic polynomial of A, At, and A-1?
Problem attached.
Problem attached.
Problem attached. (a) Find the shortest and the largest distance from the origin to the surface of the ellipsoid. (b) Find the principal axes of the ellipsoid.
Please see the attached file for the fully formatted problems. Use the inverse power method to estimate the eigenvector corresponding to the eigenvalue with smallest absolute value for the matrix -1 -2 -1 A= -2 -4 -3 2 2 1 where X0= [1,1,-1]. In finding A-1 use exact arithmetic with fractions. ln applyi
Let X be a nonempty subset of a group G. If G = <X> and H is a subgroup of G, show that H is the normal subgroup of G if and only if x^-1Hx contained in H for all x belonging to X. ALSO show that <X> is normal in G if and only if gXg^-1 contained in <X> for all g belonging to G.
Note: C means set containment (not proper) |G:H| means index of subgroup H in G U means union of sets E means belonging to Let K C H C G be groups. Show that both |G:H| and |H:K| are finite if and only if |G:K| is finite, and then |G:K| = |G:H||H:K|. Hint: if |H:K| = n, let Kh1, Kh2, ..., Khn be the distinct cosets of
"C" means set containment (not proper set containment) and "T" means intersection of sets If H and K are subgroups of a group and |H| is prime, show that H C K or H T K = {1}
Let G = RxR (R is the real numbers) with addition (x,y) + (x', y') = (x+x', y+y'). Let H be the line y=mx through the origin: H = {(x,mx)such that x belongs to R (R is real numbers). Show that H is a subgroup of G and describe the cosets H + (a,b) geometrically.
If H is a subgroup of G, define a mapping $ from the right cosets of H to the left cosets by $(Ha) = a^-1H. Show that $ is a (well defined) bijection.
If $:G->G1 is a homomorphism, show that K = the set of g belonging to G given that $(g)=1 is a subgroup of G (called the kernel of $)
Use columnar transposition cipher with keyword: Greek (keep e's in order), to decode the following message: VOESA IVENE MRTNL EANGE WTNIM HTMEE ADLTR NISHO DWOEH
Please see the attached file for full problem description. The local drug store sells a wide variety of cold medications. During the particularly harsh winter, the only three types left on the shelf were in the children's section. These are:
Is there a linear transformation T in R^3 -> R^3 for which: T[2 1 3] = [4 1 9] T[3 1 0] = [9 1 0] T[3 2 3] = [9 4 9]
I have difficulty in determining whether the signals are memoryless or causal. Please see the attached file for full problem description.
The book I am using is "Digital Signal Processing" (Third Edition) by Prokis and Manolakis. It is question 2-45 on page 144. Consider the system described by the difference equation: y(n)=a*y(n-1)+b*x(n) determine b in terms of a so that THE SUMMATION OF h(n)=1 The limits of the summation are
If K is a subgroup of H and H is a subgroup of G, is K a subgroup of G? Please justify your answer.
If X is a nonempty subset of a group G, let <X>={x1^(k1),x2^(k2)...xm^(km)|m>=1, xiEX and kiEZ for each i}. a) show that <X> is a subgroup of G that contains x. b) show that <X>C=H for every subgroup H such that XC=H. Thus <X> is the smallest subgroup of G that contains X, and is called the subgroup generated by X. note:
Q.63. For each i,j ≥ 0, define P (i,j) as follows : P (0,0) = 0, and , for (i,j) ≠ (0,0) , P(i,j) is the least integer ≥ 0 that is not equal to P (k,l) for any (k,l) with k < i and l = j , or with k = I and l < j. Find P (2987,6592).
Let T be a linear map on R^2 defined by T(x,y) = (4x - 2y, 2x + y). Calculate the matrix of T relative to the basis {α1, α2} where α1 = (1,1) , α2 = (-1,0).
Find the linear velocity of a point on the edge of a drum rotating 52 times per minute. The diameter of the wheel is 16.0in. Please show me all the steps thank you
Please see the attached file for full problem description. Write a proof for the following statement: If A is an n x n upper triangular matrix with no two diagonal elements the same, then A is similar to a diagonal matrix. Show work.
Please see the attached file for full problem description. The linear operator T: R^3 R^3 defined by T(x_1, x_2, x_3) = (x_1 - 3x_3, x_1 + 2x_2 + x_3, x_3 - 3x_1). Determine whether or not there is a basis F for R^3 relative to which the transformation T can be represented by a diagonal matrix D=[T]_F. If there is,
How to find rank of a matrix: definitions and an example (4*4 matrix) with detailed explanations. Find the rank of A= [1 0 2 0] [4 0 3 0] [5 0 -1 0] [2 -3 1 1]. Show all work.
Compute the adjoint of the matrix A below, and use this to compute the inverse of A. 2 0 4 A= 2 1 0 0 0 1
Let A be a 3x3 matrix such that At=-A(i.e.,A is a skew - symmetric). Find the general solution of the homogeneous equation Ax=0.
Compute the inverse of matrix A below, and use this to express A as a product of elementary matrices 2 0 1 A= 0 1 1 1 -1 0
Prove that if ; A is a 2x2 matrix then A2-Tr(A)A+Det(A)I=0.
Compute the inverse of the matrix below? 3 -1 -3 6 0 -2 -4 -1 3