Algebra question and answers for July 27, 2023
- Q Given the matrices A and B shown below, find -1/3A - 6B.A = [0 -18 B= [4 3 3 6] ...
- Q Suppose that v1 = (2, 1,0, 3), v2 = (3,-1, 5, 2), and V3 = (1, 0, 2, 1). Which of the following vectors are in span { v1, v2,...
- Q Given the matrices A and B shown below, find 4(A - B).A = [-5 3 5]B = [1 -2 -2]
- Q Find the product of the following two matrices[-2 -1 3 0 [1 3 4 2 - 5 -1] -3 -1 ...
- Q Suppose char. F + 3 and K/F is a Galois extension with Gal(K/F) cyclic of order 3.Show that K(C3) = F(C3, ya) for some a E F(C3).
- Q Which row of Pascal's Triangle should you use to expand (a + 3b)^7?
- Q Let A be an m x n matrix and be R. Suppose that the column vectors of A form an orthonormal set in RM. Show that the solution of the...
- Q Given that A = [-5 8] and B = [-2 10], determine the following. 9 -3 ...
- Q Let P, be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 6x - 23 - 16, 13x - 3x...
- Q Find an orthogonal matrix P that diagonalises A= and give the matrix D= PT AP.Show all calculations.
- Q Consider the space V?(R) of 2-tuple over R, then show that mapping f :V?, V? defined asf(x,y)=(x cos ? ysin ? , xsin ?+ y cos ?) is an isomorphism
- Q Let k an even natural number, k > 4. Solve in Z the equation:11 ... 121 = x.k-2 timesb. Calculate, in two ways, the determinant:cabcabA= a(b+c) b(c+a) c(a+b)a62 c2=
- Q Let k an even natural number, k ? 4. Solve in Z the equation:11 ......... 121 = x^2.k-2 timesb. Calculate, in two ways, the determinant: ...
- Q Find an orthogonal matrix P that diagonalises A = 2 2 1 2 5 2 1 2 2 and give the matrix D=P^TAP. Show all calculations.
- Q AlgebraIfR= [4 2 2 4]R is the matrix of a linear transformation consisting of a rotation with angle and a scaling. Determine ? and r
- Q Find the matrix A if (A? 2I)- = 3 1 ...
- Q For the following matrix A, Do 3 QR steps to find the approximate values of the eigenvalues ofA=7 2 32 10 63 6 7
- Q Compute the difference quotient f(x + h) f(t)/ h, h?0.(a) f(x) = 4 - 6x(b) f(x) = - 6x + 72 - 1
- Q (1) If the equation Ax = b has two different solutions then it has infinitely many solutions(A) True(B) False(2) The line { (1 2 ) + (...
- Q You have two parents, four grandparents, eight great-grandparents, and so forth.(a) If all your ancestors were distinct, what would be the total number of your ancestors for the past 39...
- Q Find the eigenvalues and the corresponding eigenspaces for each of the following matrices:
- Q Find a singular value decomposition of the matrix of AWhere, A = 1 0 06 -2 07 -4 2
- Q Which scenario could be represented by the following matrix? [10 20 40]1. The star player had 10 rebounds and 20 points in the game where the final score was 40...
- Q The navy bean soup recipe requires 120 g of bacon. If the EP unit cost of the bacon is $3.15 per kg, what is the total cost of the ingredient?...
- Q Using SVD ( singular Value Decomposition)to matrix A.A= 1 0 1 00 1 0 11 1 0 00 0 ...
- Q List the eigenvalues of A. The transformation X-Ax is the composition of a rotation and a scaling. Give the angle of the rotation, where - ?<p? ?, and give the...
- Q The dimensions of a triangular lot are 192 feet by 102 feet by 163 feet. If the price of such land is $3 per square foot, how much does the...
- Q Solve the first order homogeneous differential equationdy/dx = x-2xy/y + x
- Q A person standing 307 feet from the base of a church observed the angle of elevation to thechurch's steeple to be 56. Let a be the height of the church.Which...
- Q Let p be a prime and n be a positive integer. Then there exists a field F with exactly p" elements.
- Q Find a basis for the solution space of the following homogeneous linear system of equations. Write the dimension of each solution space. x1 + x2 - 3x3 + x4 +...
- Q Define T:R ? R by T(x) = Ax, where A = 4 -5 ...
- Q Find the volume of the cone given the measures shown."Hint: To add the pi symbol"pi
- Q Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax=b.
- Q Let A denote the following matrix:A= 1 -1 -3 4 -9 -1 7 -26 5 1 -3 14(a) Explain how...
- Q Suppose A is the matrix for T: R - R relative to the standard basis. Find the diagonal matrix A' for T relative to the basis B.[0 2 01 -1...
- Q Explain why S is not a basis for R. S = {(-6,3)}1. S is linearly dependent.2. S does not span R.3. S is linearly dependent and does not span R.
- Q For the matrix M = 3 -1 -2 0 5 4 ...
- Q The graph below g(x) is a transformation of the graph of f(x) = sin(x). There are no reflections in this graph from f(x).a. What is the period of g(x)?b. What...
- Q SupposeA = 20010 3 00 0 11 -102 0 20Which of the followings are the eigenvectors of A?(a)HUBE-{1:00- {E}] 0 [0]{AA)-{(b)(c)(d)Please check ALL the answers you think are correct.Suppose A...
- Q Find the general solution of the given system using the eigenvalue method.3] Z(0)' (t) =5-2
- Q P-1.34 Consider the matrix A of size n x n and the vector z ER",-1 ...(11)-0)A =00a. Compute Ax, ||Ax||2, and ||||2.b. Show that || A||2 ? ?n.c. Give a...
- Q Question 2. Determine whether S is a basis for the indicated vector space.S = {(1, 5, 3), (0, 1, 2), (0, 0, 6)) for Ra.b. S = {(0, 3,-2), (4,...
- Q P on R3 maps x1 = (1,-3,-4) to x2=(2,7,-8) does it uniquely determine x2? if it does, find it
- Q The initial size of a virus culture is 5 units, and it doubles its size every day. Find the general term of the geometric sequence that models the culture's size.
- Q Suppose V?, V2, V3 is an orthogonal set of vectors in R5 withV? = 35, V? V? = 24, V3 V3 = 36.Let w be a vector in Span(V?, V?,...
- Q The position of two particles on the x-axis are x? = sin t and x? = sin(t+ ?/3) where t denotes the time.(a) At what time(s) in the interval t...
- Q The graph of y = f(x) is shown below. Describe how transformations can be used to produce it from the graph of y= sin x. Then determine the period, phase...
- Q The system of linear equations { x + 9y + 7z = -3y + 2z = 2z = 4(A) has infinitely many solutions(B) has exactly 2 solutions(C) has exactly...
- Q An initial population of 4,500 undergoes a growth of 4% each month. What will the population be in 5 years?A. 47,338 B. 15,300 C.5,475 D.36,023
- Q The number of kilograms of water in a human body varies directly as the mass of the body. A 93-kg person contains 62 kg of water. How many kilograms of...
- Q Find the coordinate vector of p relative to the basis S = {P?, P?, P?} for P?p = 15 - 21x + 6x; P?= 3, P?= 3x, P? = 2x.(P)s=
- Q For the following matrix A, find a basis of its null space Null(A), and determine its dimension. Explain why vectors you find satisfy conditions for a basis.1 -2...
- Q Find the inverse of the matrix. [7 4] [9 2]Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.(A) [ 7...
- Q Find the matrix that is similar to matrix A.A=[-1-3] [1 3]
- Q Prove that if two distinct hyperplanes in R^4 intersect, then they intersect in a plane.
- Q Decide and justify whether the following real quadratic form is positive definitef(x, y, z) = x + 2xy + 2xz+ 2y + 5z
- Q Find the standard matrix for the linear transformation T,T(X, Y) = (X + 4Y, X = 4Y)
- Q The 2 x 2 elementary matrix E can be obtained from the identity matrix using the row operation r? ? r? + 2r2. Find EA if A = 4 -5
- Q The vertices of a triangle are 4(6,0), B(-6,-3), and C(0,6).
- Q Solve the equation 8x- +3 = 2(/)x. Round your solution(s) to the nearest hundredth.(a)x?2.40 (b)? 0.45 (c)? 2.21 (d)? 1.13 (e)? 0.90(f)x?-0.36 (g)x?-0.43 (h)x?-0.61 (I)x?-2.72(j)x?-4.45 (k)no solutions
- Q Suppose U, V and W are finite-dimensional vector spaces and S? L(V, W) and T?L(U, V). Prove that dim(range(ST)) ? min{dim(range(S)), dim(range(T))}.
- Q Solve the system of linear equations. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions,...
- Q Given a matrix 2 5 ...
- Q What is the effect on the graph of f(x) = |x| when the function is changed to 9(1) = |3x| + 1,A The graph is compressed vertically and shifted to...
- Q Solve the matrix equation for X: -1 0 1 ...
- Q If f(x) = 3x + 2 and g(x)= 1/3(x-1) what is the value of f[g(4)]?A 5B.-3C= 50/3D.-4
- Q All solutions [x, y, z] of the linear equation 9x- 25y + 24z = -20 geometrically represent a plane P in R. Find a normal vector n to P and...
- Q What is the initial amount for the function: f(x) = 300(1.16)^x(A) 300(B) 16(C) 1.16(D) x
- Q Let be:A := (0 -1) ? R, (1 -1)determine A?.
- Q Let be the vector from initial point P? = (-2,15) to terminal point P? = (7,8). Write v in terms of i and j .
- Q Given a matrix A = ( 2 5, -1 5, 0 1) determine matrices Q and R such that A= QR.
- Q Evaluate A = {P(1 + r)^t} / {(1 + r)^2}Click on the given link to view the question.Evaluate A when P = $9000, r = 0.05, t = 6 years.Do...
- Q Find the transition matrix from B' to BFind [x]B , when provided with [x]BB = {(1, 1, 1), (1, -1, 1), (0, 0, 1)},B' = {(2, 2, 0), (0, 1,...
- Q If A is a 3 x 3 matrix with three orthogonal eigenvectors, then A is diagonalizable.TrueFalse
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