Algebra question and answers for July 23, 2023
- Q Let V be the vector space R.(a) Let W = {(x, y, z) = R : z = x + y}. Is W a subspace of V? Give reasons.(b) Let...
- Q Determine the integers n for which the pair of congruences 2x-y = 1 and 4x + 3y = 2 modulo n has a solution.
- Q Let A = A is a 4X4 matrix . Show that A is invertible by Gershgorin Circles.
- Q Consider the linear map F: R R given byF(x, y, z, w) = (x+y+z, x+y+w, 2x + 2y).1. Find the matrix associated with F.2. What is the dimension of the...
- Q Let A = A is a 4X4 matrix. Show that A is invertible by GershgorinCircles.
- Q Let A be a symmetric 4 x 4 matrix such that det(A) = 3.Find adj(3A)A^T.
- Q Let B be a symmetric 5 x 5 matrix such that det(B) = 2. Find adj(2B) BT
- Q Let A be a symmetric 4 x 4 matrix such that det (A) = 3. Find adj (3A) AT.
- Q Use Gauss-Jordan elimination to solve the following system,3x +9y+ 2z + 12w= 1x + 3y - 2z + 4w= 2.-2x - 6y - 10w= 0,
- Q What can be said about the minimal polynomials of AB and BA.(Hint: in the singular case consider tm(t) where m(t) is the minimal polynomial of,say, AB.)
- Q Decide if the following statements are TRUE or FALSE. Write a proof for the true ones and provide a counter-example for the rest.Every linear operator T: R? ? R? can...
- Q Show that every matrix "A" with real entries can be same as symmetric and skew symmetric matrix
- Q An investor is considering three types of investments: a high-risk venture into oil leases with a potential return of 15%, a medium-risk investment in bonds with a 9% return, and...
- Q If A and B are invertible, then AB and BA are similar.(a) True(b) False
- Q Let A be a m x n matrix with m<n. Show that(a) If A has a right inverse, then A is full-rank.(b) A cannot have a left inverse.
- Q Using the surface area formula - find the surface area of a sphere.
- Q A 100 kg gilt (young female pig) gaining 350 grams of weight per day requires a diet containing 0.69% lysine. If you are formulating a diet using corn (0.3% lysine)...
- Q Solve the absolute value inequality |2x - 51-3 < 4, graph the solution set, and write the answer in interval notation.
- Q Consider a triangle ABC like the one below. Suppose that 4-30, B-72, and b=64. (The figure is not drawn to scale.) Solve the triangle.Round your answers to the nearest tenth.If...
- Q Suppose that the following system of inequalities represents the constraints in a linear programming application. Graph the feasible region on paper, thenanswer the questions that follow.9x-3y 27-3x+6y? 36x?0y?0List the corner...
- Q Let T: R ? R be a linear transformation such that T(x?, x?) = (x? + x?, 4x? + 5x?).Find x such that T(x) = (3,8).
- Q Sketch the three planes and comment on the existence of the solution System of linear equations.-2x - 3y + 2z = 33x + 2y - z = 22x + 3y...
- Q Which contract is used for a one-acre lot in an upscale subdivision?A) Farm and Ranch ContractB) One to Four Family Residential Contract (Resale)C) Residential Condominium Contract (Resale)D) Unimproved Property Contract
- Q In Texas, the statute of limitations for a non-defaulting party to enforce their rights is the event of default isA) six years for a written contract.B) four years for a...
- Q A 62-year-old widow is experiencing difficulty paying her bills. Her homestead is paid for, but she still pays property taxes and insurance, as well as other obligations on her home....
- Q A veteran may regain eligibility at the maximum entitlement if the purchaser is able to provideA) a Release of Liability.B) a Substitution of Entitlement.C) a Certificate of Reasonable Value.D) a...
- Q An aeroplane moves forward in x, sideways in y and upwards in z. Pitch is the rotation around its y-axis. Derive the rotation matrix that describes the typical 30 upward...
- Q 3.) Which of the following statements accurately describes the system represented by the matrix [ 12-73016 -20004]? A) The system has one solution. B) The system has infinitely many solutions....
- Q Performing the elementary row operations P32, M?(-) A21(2) and A14(-3) on a matrix A, we get a new matrix B where det (B) = 24. Which of the following gives...
- Q The 3 3 matrices A, B and C are such that det(A) = 2, det (B) = 3 and det(-3AB -TCT) = -72. Compute det (C) and det (AC).
- Q In triangle RST, angle S is a right angle, RS = 24 and cos R = 12/13. Find the value of cos T.Select one:a. 12/5b. 13/5c. 5/13 d. 12/13
- Q The linear systemmx + 3y - z = m2x -z = 1-2x - 3y + mz = 0is inconsistent for m = 0.TrueFalse
- Q Find the domain of the function.f(x) =10/x+8What is the domain of f?A. (-?,?)B. (-?, -8)U(-8,0)U(0,?)C. (-?0,0)U(0,?)D. (-?, -8)U(-8,?)
- Q A print shop at a community college in Cupertino, California, employs two different contractors to maintain its copying machines. The print shop needs to have 14 IBM, 19 Xerox, and...
- Q The number of cans of soft drinks sold in a machine each week is recorded below. Develop forecasts using Exponential Smoothing with a alpha value of 0.30. FI-338.338, 219, 276,...
- Q Solve the system of equations:x?+x3-x4 = 12x? + x? - 2x3+2x4 = 23x1 + x?-x3+ x4 = 32x1 + 2x3 - 2x? = 2
- Q If A is a 5 x 7 matrix with rank 3, which one of the following statements is true:A) The column space of A has dimension 2.B) The row space...
- Q Consider the following reduced matrix. This matrix represents a solution to a system of linear equations. What is the x, y, and z values for this solution?1 0 0...
- Q Use the Gauss-Jordan method to solve the following system of equations.x+y- z+ 3w= -143x-y+z+w = 64x - 2y + z- 3w= 14Select the correct choice below and, if necessary, fill...
- Q Use the echelon method to solve the given system of two equations in two unknowns. Check your answers.X/3 + y = 5/3x/7 + y =-3/7Select the correct choice below and,...
- Q A plane traveled 4760 miles with the wind in 8.5 hours and 4420 miles against the wind in the same amount of time. Find the speed of the plane in...
- Q At a concession stand, five hot dog(s) and four hamburger(s) cost $14.50; four hot dog(s) and five hamburger(s) cost $14.75. Find the cost of one hot dog and the cost...
- Q Find all subsets of the setS = {(1, 0), (0, 1), (-1,-1)}that form a basis for R2. (Select all that apply.) {(0, 1)){(1, 0), (0, 1), (-1, -1)}{(1, 0), (0,...
- Q Sketch a right triangle with ? as the measure of one acute angle. Find the other five trigonometric ratios of ?.sin ? = 5/7
- Q Use a graphing calculator to find the values of cosine and sine of each angle. Round your answers to the nearest hundredth.a. -95?b. 154?
- Q By further differentiation, identify lines with minimum y = 12 x - 2x, y = x + 4x + 1, y = 12x - 2x2, y = -3x + 3x...
- Q A sports drink was offered for sale at $3.95 at Feng's Store. At Abreu Menezes' Store, the regularselling price of a similar sports drink was $4.35.What rate of markdown would...
- Q Solve the following System using LU factorizationx? + 3x? + x3 = 42x? + 2x? + x3 = -12x? + 3x? + x3 = 3
- Q Solve the following System using x=A bX? + 3x? + x3 = 42x? + 2x? + x3 = -12x? + 3x2 + x3 = 3
- Q Use a system of three equations in three variaties to solve the problem,A woman invested a $23,000 rollover IRA account in three banks paying 5%, 0%, and 7% annual interest....
- Q Find a basis for the kernel of the linear operator:T(x, y) = (3x-y, -12x + 4y)NOTE: Using the parameter t, complete the following solution.
- Q Find transition matrix from B = {(1, 1, 1), (1, 1, 0), (1, 0, 0)} to C = {(1, 1, 1),
- Q Recall that Rm denotes the set of all m x n matrices with real number entries.How many of the following assertions are correct?(i) In a product of matrices AB the...
- Q Write the cofactor expansion for a 4 x 4 matrix down the 1st column.The terms in your expansion should look like a_{ij}C_{ij} (or similar) with specifiedvalues for i and j.
- Q Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for the dimension and in any cell of the vector.)x? + x2...
- Q Consider the line parameterized by x=5-2t, y = 3+ 8t, z= 10t. Find an equation of a plane so that the plane is perpendicular to the line and through the...
- Q Solve the linear equation system, find its particular solution and the fundamental solution of its corresponding homogeneous linear system. Find the general solution.2x14x2 + 5x3 + 3x4 = 13x16x2 +...
- Q A building that is the nearest 50.65 feet. tall has a shadow 55.48 feet long. Find the angle of the Sun to the Sen elevation of hundreth of a degree.
- Q Maximize P = x + 2y - zsubject to2x + y + z ? 144x + 2y + 3z ? 282x + 5y + 5z ? 30x ? 0, y...
- Q Show that there are no square matrices A and B such that AB-BA=1.
- Q Maximize Q = xy, where x and y are positive numbers such that x+6y = 2.
- Q Us a the graph of y = ex to evaluate e 2 to four decimal places.
- Q Use Cramer's rule to solve the following system of equations. If D = 0, use another method to complete the solution.5x + 3y = - 42x + 3y = -7Write...
- Q Determine whether the statement is true or false.x + 2 is a factor of P(x) = x + 2x - x - 2.
- Q Let A = 1 -2 Q = 1/?2 -1/?2 1 4 ...
- Q The matrix A= 1 -1 1 1 defines a transformation of R. Select all true...
- Q Find the transformation, given by the matrix A, which stretches by a factor 5 and reflects over the line y = x.
- Q List five vectors in Span (V? V?}. Do not make a sketchv1= 9 v2= -6 2 ...
- Q We start with functions y?= 5x and y? = 2x+3x. First, explain to me why the set {y?, y2, Y3} where y3 = x-3x is a linearly dependent set. Second,...
- Q be T: R3 R a linear transformation that satisfiesT(1,1,4) =(-1,-1) and T(3,-6,4)= (1,1)if v = (15,-21,4)then T(v) = (x,y)where "y" is:
- Q For each of the systems of equations that follow, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in row echelon form. Indicate whether the system is...
- Q a) For the following set of linear equations:10x? + 25x2x3 = 2-3x? - 6x? + 2x3 = -6x? + x2 + 15x3 = -4a) Show two iterations of the Gauss...
- Q Let A and B denote matrices whose sizes are appropriate for the following sums andproducts, which of the following is correct ( )(A) (AT)T=A- (B) |A|=|AT| (C) (AB)T=ATBT (D) (AT)T=AT
- Q Let A be a 4x4 matrix with row vectors a?, a2, a3, a4 and determinant 2.Find the determinant of the matrix with row vectors a? + a?, a? + a2,...
- Q Suppose A is a 4 x 3 matrix, B is a 3 x 5 matrix, and C is a 4 x 5 matrix.Which of the following matrix operations are defined?...
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