Algebra question and answers for July 28, 2023
- Q Consider points A(1,4,7), B(2, -1,3), C(3, 5, 3), A'(2,3,5), B'(1, 1, ?1)and C'(1, -4,-2).Find a point P and a line h such that triangles ABC and A'B'C' are in perspectivefrom...
- Q (1 point) Find the matrix A of the linear transformation T from R2 to R that rotates any vector through an angle of 135 in the counterclockwisedirection.E
- Q On the graph of f(x) = sinr and the domain 0 < x < 2, for which of the following intervals is f(z) strictly decreasing?Choose all correct answers.Select all that...
- Q The number of hours of daylight in Boston is given by[365 (x-79)] + 12,h(x) = 3 sinwhere x is the number of days after January 1. (1 point for each...
- Q 5. You are given three vectors below. It is known that these vectors are on the same plane. Determine the value of t=? (15 pts)183A) t = -4 B) t=0...
- Q Is q=0.50.6a steady-state vector for A=0.4 0.50.6 0.5? Justify your answer.Select the correct choice below and, if necessary, fill in the answer box to complete your choice.OA. The vector q...
- Q In class, we discussed how a point and a nonzero vector emanating from itcompletely determine a line. Explain how this affine representation (point plusvector) is equivalent to those of symmetric...
- Q 22. Suppose that A M4x4(R) and b R areA=1 2 1 -1123 5365 21222(a) (2.5%) What is N(A)?(b) (2.5%) What is the solution x of Ax = b?and b=
- Q The point (2, -1) is on a function. State the corresponding point on the inverserelation.a) (-1, -2)Ob) Can't find it without the original function.Oc) (-1,2)d) (1, -2)
- Q Simplify. Write the answer using positive exponents.XWhat is raising a quotient to a power?OA. For any numbers a and any integers m and n, (am)" = amnB. For any numbers...
- Q Find the intersection of the following planes by letting z = t.5x - 4y + z-1 = 0X-Z+3=0
- Q Let u= (-2, 6, 1).Find ||u||. Use that to find a unit vector that points in the direction of u. Write your answers in exactform, using sqrt() to indicate square...
- Q Solve the system of equations using Gauss-Jordan elimination.x+2y-z = 02x + z = -1x - y = 1a. Write the system of linear equations as a matrix equation Ax =...
- Q Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form.-9x1...
- Q Evaluate 2x -y for the given replacement values.x = 2 and y = -92x-y=
- Q products may differ. Describe qualitatively the solutions to the matrix equation X - X = Owhere X is a (2 x 2) matrix and is the zero matrix. Hint. Set...
- Q A doctor's prescription calls for a daily intake containing 40 mg of vitamin C and 10 mg of vitamin D. Your pharmacy stocks two compounds that can be used: one...
- Q If u and are linearly independent, then u +, u are also linearly independent.TrueFalseJustification:
- Q why is a system with 50 equations and 51 variables is guaranteed to contain atleast one varable?
- Q Consider the following 2*2 system:2x? - x? = 1-x? + 2x? = 0a) Rewrite the linear system in the matrix format Ax=b .b) Solve Ax=b with inner product, and show...
- Q Let a= (1, 2, 5) and b = (3, 3, k).Find k so that a and b will be orthogonal.
- Q (a) The zero vector is orthogonal to all subspaces.(b) If one of the eigenvalues is zero, the matrix is singular.(c) Suppose the eigenvalues are 1, 2, 3, the matrix is...
- Q Consider the set W of all 2 x 2 matrices A such that both (1, 2) and (2, -1) are eigenvectors of A. Prove that W is a subspace of...
- Q A real quadratic form in three variables is equivalent to the diagonal form 6y + 3y+ Oy. Then the quadratic form isPositive semi-definitePositive definiteIndefiniteNegative definite
- Q Factor completely, or state that the polynomial is prime.x +81Select the correct choice below and fill in any answer boxes within your choice.A. x +81 =B. The polynomial is prime.
- Q Construct a triangle of sides 68, 58 and 42 mm long respectively. Bisect the angles tofind the centre of a circle that will touch the three sides of the triangle....
- Q Solve the formula for the variable h.f=9ghh=
- Q Take A= 3, B=1, C=4Find the orthogonal projection matrix P onto the plane ax + by - cz = 0 (a, b, c are defined in the instructions)
- Q 1 3 00 2 41 5 41 1-1a) (7 points) What is the basis for the Row(B)?3. Let B=b) (7 points) What is the basis for the left null space...
- Q Find an orthogonal basis for the column space of the matrix to the right.-1 5 51 -7 41 -1 71 -3 -4An orthogonal basis for the column space of the...
- Q Suppose that S={(-1,1,0), (2,2,0), (0,0,3)} is orthogonal basis for a subspace W of R.Find the orthogonal projection of u in W where linear combination of the basis vector isu =(2,1,3).
- Q Solve the initial va problem xi-Axt) for 120, with x0) (2.1) Classify the nature of the origin as an attractor, repeller, or saddin point of the dynamical system desobed by...
- Q Consider the two points A = (-1,2) and B = (1,8) to be points on the curve.a) Give a possible formula for the function of the form y = a(b)...
- Q Write the decomposition of a vectorX(-5; 4; 0), (0; 1; 2), (1; 0; 1), F(-1; 1; 0).Solve the task and fill in the required fields.Ansver:A=A?=X?=in terms of vectors P. 9,7...
- Q Using the matrix U = [U?U?U3], determine whether or not the columns of U span R. Explain your approach.Solution:%code
- Q Write the decomposition of a vectorX(-5; 4; 0). p(0; 1; 2). ? (1; 0; 1), 7 (-1; 1; 0).Solve the task and fill in the required fields.Answer:4?=x?=in terms of vectors...
- Q What is the solution of the system of linear equations[a?x+?y=b?[a??x + a??y = 6?a. The solution of SLE is a set of the ordered pairs of numbers (y; x).b. The...
- Q Solve the following system{3x + 5y - 7z = 8 (mod 83)9y + 13z = 13 (mod 83)8x-9Y+13z=13 (mod83)7x + 4y + 5z = 15 (mod 83)...
- Q Simplify the expression by combining like terms.7m+4m
- Q Let V=R and B be the ordered basis,B =[ 1 [-1 1 ] 1]Find the coordinates of the vector, V = 1 ...
- Q Select the inequality that is equivalent to the given inequality.-7x ?14Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer.a x ? -2b...
- Q Solve the equation using the quadratic formula.2x-9x-1=0
- Q Determine the values of k such that thesystem of linear equations does not have aunique solution. (Enter your answers as acomma-separated list.)x + y + kz = 6x + ky...
- Q We have a matrix a find a, b, c such that the matrix is a quadratic form
- Q Use Cramer's rule to solve the system.X +y-z = -4x - y + 2z = 14x + 4y 2z = -17Find the determinants.D =Dx=Dy=Dz=Select the correct choice below and fill...
- Q Describe how to transform the parent function y = x to the graph of the function below. Choose all that apply.y = -2(x + 3) + 1Select one or more:a....
- Q Consider the following observation modelwhere [by 1 b? = 5 b3 = 3 b4 =4)= 4)(a) x2.04, 4.52,-0.24](b) x-2.04(c) x 6.45(d) x [6.45, 4.52. -0.85]b? = I? +23+7?b?r2-2r3+ n?b3=11-423+ngb?2r1 +223...
- Q This set of questions pertains to reference angles.a. Name 3 different angles which could have a reference angle of 20 degrees. How did youarrive at this answer? 2-3 sentences.b. What...
- Q Find a basis for, and thus the dimension of, the subspace of R given by the plane * - 3y + 5z = 0. Why would it make no sense...
- Q Evaluate (without use of a calculator).(a) log4 2 + log4 128 =(b) log4 112- log4 7
- Q (a) Let A be an invertible n x n and suppose that A-1 = A. Prove that det(A) = -1 or det(A) = 1.(b) Let A be a square matrix...
- Q 0.0116 0.0046 0.00230.0023 0.0046 0.0116Let D= 0.0046 0.0093 0.0046 be a flexibility matrix, with flexibility measured in inches per pound. Suppose that forces of 40, 10, and 20 lb are...
- Q (a) Suppose that A is a 3 x 3 diagonalizable matrix with a basis of eigenvectors of R given by {u?, U?, U3} with corresponding eigenvalues A1, A2, A3. Suppose...
- Q Calculate the inverse A^-1 of the matrixA = ( -1 2 2) (2 -1 2) (2 2 -1)
- Q Find the matrix P that orthogonally diagonalizes A. Compute P-AP.A = 3 2 4 2 0 2 4 2...
- Q Find 2A + 3B.a=[4 8] b=[-5 9] [1 7] [5 -8]
- Q Matrix A represents the number of points scored in each quarter for the first 4 games of football played by WCHS. Matrix B represents the number of points scored in...
- Q Solve each system of equations using elementary operations.a. (i) x + y + z = 0 (ii) x - y = 1 (iii) ...
- Q For each, determine the amplitude, the axis of the curve, the range, the period, the phase shiftand the zero(s) within one period. Keep your solutions neat and organized. (7 marks...
- Q A n x n Hermitian matrix contains exactly k real entries. Show that k + n must be even.
- Q Solve using Cramer's Rule.- 5x + 2y + 3z = 276x + 6y + 5z = - 32-5x + 3y + 3z = 25The solution of the system is(Type integers...
- Q Solve using Cramer's Rule.3x-y = 7x-3y=9What is the solution of the system?(Simplify your answer. Type an ordered pair, using integers or fractions.)
- Q Solve the following system of equations using Gaussian or Gauss-Jordan elimination.- 10x-3y = - 17 4x + y = 7Select the correct choice below and fill in any...
- Q Without graphing, classify the system as independent, dependent, or inconsistent.12y - 3x = 218y = 2x 14
- Q rite the equations for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to the graph of g(x).
- Q 1. A student took 60 minutes to answer a combination of 20 multiple-choice and extended-response questions. She took 2 minutes to answer each multiple-choice question and 6 minutes to answer...
- Q Write an exponential function to model the following situation. A population of 120,000 grows 5% per year for 14 years. How much will the popluation be after 14 years? Write...
- Q Show that AX = XA where is a diagonal matrix whose diagonal entities are eigenvalues A =And also show that X-AX = AA= ?1 ...
- Q If the determinants |A| = 3 and |B| = 2, find |2(AB) for 5x5 matrices A and B.
- Q Without graphing, classify the following system as independent, dependent, or inconsistent.2x - y = 26x - 3y = 6Choose the correct answer below.A. The system is dependent.B. The system is...
- Q Suppose A E Rnxn, AT = A, and (x, Ax) ? 0, Vx ER". Show that (z, Az) ? 0, VzE Cn
- Q If the determinants |A| = 3 and |B| = 2, find |2(AB)-| for 5x5 matrices A and B.
- Q The given sot is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W An orthogonal basis for Wis(Type a vector or list...
- 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...
- Q Write down the 3 x 3 elementary matrix corresponding to the row operation ? ? 1-2r3.Write down the inverse of this matrix and explain briefly, in terms of row operations,...
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