Algebra question and answers for July 24, 2023
- Q Consider the linear subspace U of R4 generated by {(2,-1,3,-2), (-4,2, -6,4)}. The dimension of U isa) 1b) 2c) 3.d) 4
- Q Let k ? R and consider the linear system in the unknowns x, y, z:kx + 2y+z=0y+z=03z = 0Find all values of k for which this system has(a) a unique...
- Q Answer each of the following as True or False justifying youranswers:c) The inverse of a non-singular matrix A is unique
- Q Find the basis and rank of the vector system. Express non basis vectors with basis vectors: a1=(-2;3;4;11), a2=(7;-2;3;4), a3=(1;-3;-5;-13), a4=(3;2;7;16)
- Q Use matrices to solve the system.3x +2y-z = 11.65x -3y + 2z = -7.7-2x + y - 2z = 6.7
- Q Use matrices to solve the system.2w + 2x +2y+z=-23w+ 4x + y2z = -104w + 3x - 2y + 2z = 22w - 2x+3x = 7
- Q Find a unit vector that has the same direction as the given vector.v=-5,6
- Q Suppose A R5x5 has det(A) = 10. Determine det (2A) and explain your answer.
- Q Given the matrix A 1357. What is the inverse of A?A. -187-3-51B. 187-3-51C. -167-3-51O. 167-3-51
- Q Suppose Amanda, Claudia and Delaney go to a donut shop.Amanda buys 6 apple crumb, 6 brown butter pecan and 2 chocolate frosted donuts and ends up spending $19.56.Claudia gets 5...
- Q Find the linear function, f(x), passing through the points: (-10, 10) and (8, 10)Enter your answer using function notation.
- Q ABC is a triangle. Pis a point on BC such that BP: PC=3:2 and Qis a point on AB such that AQ: QB=1:2. Line AP and CQ intercept at R....
- Q Let A, B be 4 x 4 matrices with |A| = -2 and |B| = 5.Calculate|- 2A B AT |.
- Q Let A = [110] b = [3] Find A^-1 and use it to solve the system Ax = b.
- Q Let V = R? and let W be a the subspace of all (a, 0, b, 2a +b, -3b). Find a basis for W. Select the correct answer form the...
- Q Consider the following 3 x 3 matrix:[? 1 7 ? 3 2 4 -1 1]Find the values of for which the matrix is:1. positive definite2. positive semidefinite3. negative definite4. negative...
- Q Use the inner product< p,q>= p(-1)q(?1) +p(0)q(0) + p(3)q(3) in P? to find the orthogonal projection of p(x) = 4x + 5x - 7 onto the line L spanned by...
- Q if A is a regular matrix, then A+A? is positive definite
- Q Given A= [-2 -3] and B= [5 2] [5 2] [1 -1]use the Frobenius inner...
- Q Write the eigen values and eigen vectors corresponding to the linear map represented by the following matrix.A = 3 0 8 -1
- Q 4. Determine whether the given matrix is invertible without computing its determinant.-1 -3 0 1 3 5 8 -3-2 -6 3 20 -1...
- Q Show that every group of order 567 has a normal subgroup of order 27.
- Q Let P : R ? R be the skew-projection onto the plane II = {-(4x + y + 3z) = 0} parallel to the vector (1, ?2, 4).Find bases for...
- Q Use Gauss Jordan to find the solution of system of Linear equations. Use elementary row operations in your solution.x -2y+ z = -1x + 3z=-11-4x + 7y + 4z =...
- Q Let A = 0 -1 2 2 Find PLU factorization. -1 3 4 1 ...
- Q Consider3x + 3y + 3z=- 3k4y + 8z= -4x + 4y +7z = 4ka) Using Gaussian elimination method find all value(s) of k such that the system becomes consistent.b) Using...
- Q 3) Find the values of x and y using pseudoinverse.X + 3y =175x + 7y =1911x + 13y =23
- Q Plot the ordered pair (1,-1). State in which quadrant or on which axis the point lies.Plot the ordered pair on the graph to the right.In which quadrant, or on which...
- Q Identify the intercepts.What are the intercepts?(Type an ordered pair. Use a comma to separate answers as needed.)
- Q Solve the system of linear equations by graphing.y = 4x3x-y=1Use the graphing tool to graph the system.
- Q Confirm that B is an orthonormal set, and find the projection of v onto span BB= 1/?6 -1 , 1/?3 1 and v= 8 ...
- Q Which of the following was NOT an aspect of Taoism practiced in China?A. Cultivation of chiB. Use of alchemyC. Respecting social relationshipsD. Ancestor worship
- Q 3. Complete the following questions using the following planes T?: 2x + 4y-6z -2 = 0 T?: 7x+14y-21z-7=0 R3: 4x+8y-11z +5=0 a) Determine the normal vectors for each of the...
- Q Use the Gram-Schmidt process to find orthonormal bases for the spaces
- Q Find the 3x3 matrix that produces the described composite 2D transformation below, using homogeneous coordinates. Rotate points through 45 about the point (6,9).
- Q Consider T(x,y) = (2x-y, -4x+2y), is T invertible? Why or why not? If so, compute the inverse, T-1, and compute the image of 8 under the inverse map. ie. Compute...
- Q 6-Which of the following statements is true(a) det A = det A-(b)det(A + B)=det(A)+det(B)
- Q Perform the indicated operation, if possible.[4 8 5 -9 + [ 7 1 -11 36 -1 12 1] - 3 8-10 9]Select the correct choice below and, if...
- Q The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these products exist.A is 2 x 5, and...
- Q Solve the following system of equations. Let z be the parameter.3x+2y-z=24x + 3y +z = 5Select the correct choice below and, if necessary, fill in the answer boxes to complete...
- Q To find the product matrix AB, the number of of A must be the same as the number of of B.To find the product matrix AB, the number of of...
- Q Use the echelon method to solve the system of two equations in two unknowns. Check your answers.6x - 5y = -98x - y = 5Select the correct choice below and...
- Q Use the Gauss-Jordan method to solve the system of equations.y=x-1y=5+zz=0-xSelect the correct choice below and fill in any answer boxes within your choice.A. There is one solution. The solution is...
- Q Fill in the blank with the correct answer that completes the following sentence.on a matrix correspond to transformations of a system of equations.on a matrix correspond to transformations of a...
- Q Solve the following equations:a) tan (x-72) = -1 on the interval (-?,?).b) 2cos (x/3) + 1 = 0 on the interval [0,27).c) 2cos^2(x) -3cos(x) +1 = 0 on the interval[0,2?)
- Q Gonzalez Manufacturing borrowed $24000. Part of the money was borrowed at 8%, part at 10%, and part at 12%. The annual interest was $2480, and the total amount borrowed at...
- Q Let Z={1,2,3,4}. Let A be the following group of permutations on Z,{(1), (23),(24),(34),(234),(243)}Prove that the subgroup B={(1), (234), (243)} is normal.Give the operation table for the quotient group A/B.
- Q Consider the quadratic form q(x?, x2, x3) = 6x1 + 4x1x2 +9x2 + 7x3.3.a Find the matrix A of this quadratic form. What is the definiteness of q(x)?3.b Find the...
- Q Suppose v?, v2, v3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v?, v?, v3) such thatv?.v? = 18, v?.v2=131, v3.v3=16,w.v? 90, w.v?=524, w.v3=-32,then...
- Q Matrix A is singular. True or false?A= 1 2 -1 2 -1 3 3 1 2TRUEFALSE
- Q Find a) the characteristic equation and (b) the eigenvalues and eigenvectors of A below, then decide whether or not A is diagonalizable. If not, explain why not. A= [5 8...
- Q Find B-AA= 8 4 B= -7 5 9 9 4 ...
- Q Write an augmented matrix for the following system of equations, and state the dimension of the augmented matrix.3x-2y+3z = -13x-9y+7z = 79y-9z = -2
- Q The subset in the form [x y], where x and y are real numbers, is a subspace of R2 ifSelect one:x = 0 and y ? x.None of thesex ?...
- Q Solve the linear system by Gaussian elimination:x- y + 2z - w = -12x - y-2z- 2w = -2-x+2y-4z + w = 13x + 2aw...
- Q Provide the missing information.Explain the meaning of the notation R? = R3.
- Q The real zeros" can be described as follows (if the zero is not an integer, type the fraction form, not the decimal formA real zero is Does the graph cross...
- Q Construct the equation of a 4th degree polynomial with real coefficients that has the following characteristics: the only zeros are 1/3, -4, and 2 the graph should "bounce off" the...
- Q Question2: (20 points): Let v? = [2 -2] and v? = [3 -2] be two vectors in R2.(a) [10 pts] Determine whether v = [2 -2] belongs to span {v?,...
- Q Question 1 [20 pts] Let W be the set of polynomials of the format + bt + c.a) Does p(t) = t + 4t - 4 belongs to W?b) Is...
- Q Let A and B be row-equivalent matrices.(a) Show that the dimension of the column space of A is equal to the dimension of the column space of B.(b) Are the...
- Q Solve the system of equation by the method of your choice. If the the system has a unique solution, type in that answer as an ordered triple. If the system...
- Q 4. The set W of polynomials of the form a? + a?x + a?x + ?3x + ??x4, where a = a? and a? = a3 is asubspace of P4....
- Q AlgebraS = {(6,-7,8,6),(4,6,-4,1)}(a) u = (-42,113,-112,-60)check whether the set S is a basis or not
- Q Solve the system.x+y = -4y+z=1x-z = -5Is the system inconsistent, dependent or does it have 1 solution
- Q Let T: R R2 be the linear (matrix) transformation defined by: T(x1, x2) = (-7x1 + x2, 6x1-4x2,8x1 +5x2,-9x1- 2x2). Determine the standard matrix A of the linear transformation.
- Q If A is a m x m matrix and rank (A - Im) = m - 1. Show that is an eigenvalue of A with multiplicity of at least one.
- Q Let T: R ? R be the linear (matrix) transformation defined by:T(x1,x2)=(-7x1 + x2, 6x1-4x2, 8x1 + 5x2, -9x1 - 2x2).Determine the standard matrix A of the linear transformation.
- Q LetA = 2 9 -2 61 6 -1 4Find an orthonormal basis of the kernel of A.
- Q You are holding a kite string in your hand. The angle of elevation from your hand to the kite is 53and the distance to the kite is 300 feet. Your...
- Q Suppose a firm produces three outputs, y1, y2 and y3, with three inputs z1,z2 and z3. The input-requirement matrix is given by A = [ (3 12 )(2 5 1)(...
- Q For the following system of homogenous linear equations:x-y-11z=02y-13z = 0Use elementary row operations to solve the above system. Identify the free variable(s) if any.
- Q Given the planes P?: 2xy + 5z = 8 and P?: x-y + 2z = 4, and given the point A(5, -3,2).(a) Find the cosine of the angle between the...
- Q Let T: R6 ? R6 be linear transformation such that T(x)= Ax and det(A) 0. Find therank(T), range(T), kernel(T) and nullity (T)Rank (T)Range(T)Kernel(T)Nullity(T)
- Q You are given the following set of data points.x 0 2 3y 2 ...
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