Algebra question and answers for July 26, 2023
- Q Solve the system of two linear inequalities graphically.{ x > -4{ y ? 1
- Q Give a geometric description of Span (v? , V?) for the vectors (A) Span (v?, v?) cannot be determined with the given information.(B) Span (v? , v?) is the plane...
- Q Solve using Gaussian or Gauss-Jordan elimination.W+ x + y + z = 53w+ 3x-3y 3z=94w 3x + 3y + Z=14W-x + 5y + 4z = 8(A). The solution is (B)....
- Q Find a matrix P that diagonalizes A, and compute p-AP.
- Q Consider the matrix A = 3(a) Compute the adjoint matrix adj(A).(b) Compute the determinant det(A) and find the inverse matrix A-,Consider the matrix B= 2 1(a) Use the cofactor exapansion...
- Q Compute the product of the following partitioned matrices using block multiplication.
- Q Let T be a linear transformation from R to R defined by T(x,y) = (2x -y, x + y).a) Find the matrix of T with respect to the bases B?...
- Q Compute the eigenvalues of A using un-shifted QR algorithm.Can you get improvement by using the shifted version of QR algorithm? Show your work.
- Q Use the inner product (p, q) = aobo + a?b? + a2b? to find (p, q), ||pl|, |la||, and d(p, q) for the polynomials in P2.p(x) = = 3- x...
- Q Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(7).
- Q Let A = {a?a2 a3} and B = {b? b2b3} be bases for a vector space V, andsuppose a? = 3b?-b?, a2 = -b? + b? + b3, a3 =...
- Q Change each degree measure to radian measure in terms of ?1) 1352) 3003) 210
- Q Prove that if the matrix A has orthogonal columns, then Az = b has a unique least squares solution, and find this unique solution.
- Q Find the first & second derivatives of the following functions:a) f(x) = Q^(?)b) f(x)=(Y?-1)/Y?
- Q Let A=(?? ? ? ??). Find the singular value decomposition (SVD) of A
- Q A store is having a sale on almonds and jelly beans. For 5 pounds of almonds and 3 pounds of jelly beans, the total cost is $23. For 2 pounds...
- Q Find the values of x, y and Z such the matrix below is skew symmetric. 0 X 3 ...
- Q Compute all the minors and cofactors of1 2 32 0 1`2 3 4
- Q Consider the equations5x? + x? + 3x? + 6 = 0-5x?-2x? +7= 0.Apply Gaussian elimination to convert this system into (row) echelon form.Find the general solution and write it as...
- Q Given that f(x)=1x-4, the vertical asymptote(s) of f is: X=?
- Q Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix.1 4 -2 50 1 -5 5x= x?_ + x?__(Type an...
- Q Solving the following system of equations using any method. Show each step clearly.X + 2Y + 4Z = 112X + Y + 2Z = 73X - Y - 2Z =...
- Q PrecalculusFind the vertex, focus, and directrix of the parabola. Graph the equation.2y+8y-4x+6=0
- Q Solve each initial-value problem.y" + 2y' + 5y = g(t); y(0) = 1, y'(0) = 2y" - y' - 6y = {t, if t < 2; ...
- Q Find the vector equation of the line through the point (-4,7,-2) parallel to the vector [3,5,-5).You may use x to abbreviate the general position vector [x. y, z). Both the...
- Q B) Please explain sine, cosine and tangent in the context of angles on the coordinate plane. Again, describe the ratios and what they mean. Please use at least 3 sentences.C)...
- Q The histogram below shows the scores for Mrs. Smith's first block class at Rock Middle School. If an 85 is the lowest score a student can earn to receive a...
- Q Determine the eigenvalues of the matrix [3 -3] . Find at least one corresponding eigenvector from the eigenvalue that you have determined. *you may attach your scanned solution or input...
- Q Let (V, (,)) be an inner product space and let f, g be vectors in V. If||f|| = 4, ||g||= 5 and || f + g = ?31, then what...
- Q ThinkingFind AN unit vector that is perpendicular to the yz-plane and perpendicular to the-2i+7j - 3kvectorKeep your answer in exact form.please show all work. thanks.
- Q Let A be a 3 x 8, B be a 8 x 7 and C be a 7 x 3 matrix. Determine the size of the following matrices (if they...
- Q Austin is going to invest in an account paying an interest rate of 2.2% compounded daily. How much would Austin need to invest, to the nearest hundred dollars, for the...
- Q Let T: M??? M?? be defined by T([a b]) = [ 2c a+c] c d b-2c ...
- Q If ?=5?/2, then find exact values for the following. If the trigonometric function is undefined for ?=5?/2, enter DNE.A. sec (0) equals ____________B. csc (0) equals ____________C. tan (0) equals...
- Q Which of the 8 symmetries of a unit square are symmetries of a taxicab circle
- Q Let A be an n x n matrix where n is odd and such that A = -A^T.(a) Show that det(A) = 0.(b) Does this remain true in the case...
- Q -1 2 0 4 1 4 1 -3 ...
- Q a = <-3,-5> and b = <1,4>.Represent a + b using the parallelogram method.Use the Vector tool to draw the vectors, complete the parallelogram method, and draw a + b.To...
- Q Which of the following statements are true?A. If the columns of an m X n matrix A span R?, then the equation Ax=b is consistent for each b in R?.B....
- Q Factor matrix A into E's so that A = E?E?...EnA= 1 2 4 6
- Q Find the optimal row and column strategies and the value of the matrix game.5 -1 14 2 3-2-3 1
- Q Let. 0 3 3 A= 1 1 0 -1 2 3Assume that AB =...
- Q Suppose, a = 10i +14 j and b = ki +17 j9.1) Find the exact value of k such that a and b are parallel.Answer:You have not attempted this yet9.2)...
- Q Solve for X in the equation 3X + A = B, whereFind the focus and directrix of the parabola y=-2x. Then sketch the parabolaFind the standard form of the equation...
- Q Which of the following is always equal to the inverse of (AB) ?(A) B- + A-(B) B-A-(C) A- + B-1(D) A-B-1
- Q Use the table below to find:(fog)(5) =(gof)(8) =(fof)(-2)=(gog)(0)=x -2 0 4 5 7 8 ...
- Q Let F = (4z+4x)i + (4y + 4z + 4 sin(y))j+ (4x + 4y + 4e?) k(a) Find curl F.(b) What does your answer to part (a) tell you about...
- Q Show that the columns of the 3 by 4 matrix A [with rows] = (1 1 1 1) (1 2 ?1 3) (1 0 3 ?2) ? M??(Q) span Q....
- Q The matrix -3 3 A = 5 5has a singular value decomposition A = U?V? where...
- Q Let us consider the following matrices.Calculate the following. If a result does not exist, explain why.[a] AB[b] AC[c] BC[d] CB[e] BD[f] CD
- Q Which of the following pairs of vectors is a pair of independ2 -5-1 -2Select one:A {(1,2),(-5,1)}B {(1,1),(-5,1)}C. {(1,1), (2,1)}D. {(2,1),(-5,1)}
- Q Let A = [-1 1] [1 1] [1 -2]Which of the following vectors are not in the subspace {As :...
- Q Sketch several periods off(x) = sin(?x) within -1/2<x<1/2and expand it in an appropriate Fourier series.
- Q If possible, find AB, BA, and A. (If not possible, enter IMPOSSIBLE.)A = 1 4 , B= 3 -1 2 4 ...
- Q Consider the systemx? = x? + sin x?x? = ?x + uy = x1where the parameter is not exactly known but can be bounded as follows:|?| ? 2Design a sliding...
- Q Find A? and C? by using Eigenvalues and Eigen-vectors:A=[1/-2+1/4] C=[1/1/4 +2/0/-4 -1/1/5]
- Q The set B=(1-t,2t-t-t-t) is a basis for P?. Find the coordinate vector of p(t)=-1+13t-6t relative to B.(P)B= 4 5 -3
- Q Given a system of two linear equations into variables, find the solution of the system algebraically and graphically. Solve by graphing, substitution method, and elimination method.4x +3y=7x-2y = -1
- Q By using de Moivre's Theorem, prove thatcos5? = 16 cos?? - 20cos? + 5 cos?Hence find all the roots of the equation48x? - 60x + 15x + 2 = 0.
- Q A woman is m years old. How old will she be in ter years' time?
- Q SOLVE Linear Regression using quadratic nonlinear polynomial regressing model,then find the RS, RT, R and R.n=7 ?x?y? = 1 ?Xi= 119.5 ?Xi= 140 ...
- Q You are shown a graph of two lines that intersect once at the point equation, (-3/7, 7/3) what do you know must be true of the system of equations?.
- Q Select the correct choice below and fill in the answer boxes within the choice.A. There are 2 possible solutions for the triangle.The measurements for the solution with the longer side...
- Q Graph the following function.y = 4 cos (x + ?/8)
- Q Write "T" or "F" to indicate true or false if vector u is a linear combination of the vectors in the set S. If ? can be expressed as a...
- Q Use the definition of a logarithm to rewrite log?36 = x in exponential form. Do not solve.
- Q Determine whether the eigenvalues of each matrix are distinct real, repeated real, or complex.[7/-20 +4/-11][3/3 -4/1][26/-60 +12/-28][-1/-4 +/1-5]
- Q Suppose matrix A is a 4 x 4 matrix such that A.[-18/24/36/-24]=[-3/4/6/-4]Find an eigenvalue of A.
- Q The corresponding linear combination would be: is a linear combination of the set S containing the vectors
- Q 4 1 2 A = 0-3 3 0 0 2Describe the set of all solutions to the homogeneous system Ax = 0.Find A?, if it exists.a)...
- Q Let T: R? R be a linear transformation defined by T(v) = Av, 1 0 0 A = 1 0 -1 Find T(3,1,-1)...
- Q Given v? and v? in a vector space V, let H= Span {v?, v?}. Show that H is a subspace of V.
- Q Solve the following system analytically. If the equations are dependent, write the solutions set in terms of the variable z.x-y+z= -78x+y+z=8Select the correct choice below and, if necessary, fill in...
- Q Write the system of linear equations in the form Ax= b and solve this matrix equation for x.-2x?-3x? = -11 6x?+ X?=-39
- Q Suppose that ?? = (2,1,0,3), ?? = (3,-1,5,2), and v?= (-1,0,2,1). Find the vector spanned by vectors ??, ?? and ??
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