Algebra question and answers for July 25, 2023
- Q Find a subset of the vectors v? = (0,2,2,4), v? = (1, 0,-1,-3), v? = (2,3, 1, 1) and v? = (-2, 1, 3, 2) that forms a basis for...
- Q Consider the following matrix: A = 4 0 1-1 1 0-2 0 1a) Find the eigenvalues of Ab) Using the eigenvalues of A, find the corresponding eigenvectors
- Q Let v?= [2 v?= [10 v?= [-6 , and y= [-4 -1 -4 ...
- Q Determine whether the set {P?, P?, P?} is linearly independent in P?, where p? = 2+x+3x + 4x, p? = 4 + 3x + 2x + x and p? =...
- Q Write the system of linear equations in the form Ax=b and solve this matrix equation for x.x?-5x?+2x?=-5-3x?+x?-x?=2-2x?+5x?=11
- Q Let A be an invertible 2 x 2 matrix. Find a general formula for A- in terms of the entries of A.
- Q Let the function f be given by f(x) = x ? 5x + 9x ? 4 and A = 1 -1 0 2 3...
- Q Rewrite log ? 64 as a logarithmic expression with an argument of 4.
- Q Let Q be an nxn invertible matrix and {u?, U2,..., uk} is a set of vectors in R. Prove that {u?, 12,..., uk} is linearly independent if and only if...
- Q 2) Shou that the Projection onto the vector v = [1, -2,1] is a linear transformationT: R R3b) Find the Standard matrix [T] for this transformationC) Find the nullity ([T])...
- Q Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below.A= -3 -4 ...
- Q Consider a scalar valued functiong(W) = 4w?? +6w??+6w??+9w?? of the 22 matrix W = {wij}.(1) Express the matrix form of g (W).(2) Find the matrix gradient of g (W) with...
- Q Find all unit vectors u E R that are orthogonal to both v? = (2,7,9) and V? = (-7,8,1).
- Q Suppose the augmented coefficient matrix of a certain linear system is: [1 1 3 ? -3]...
- Q Rewrite log 3 ?10 as a a logarithmic expression with an argument of 10.
- Q the following sum is a right riemann sum for a certain definite integral using a partition of the interval [1,b] into n subintervals of equal length then the upper limit...
- Q Find the equation y = Bo + B?x of the least-squares line that best fits the given data points.(4.3). (5,2). (7.1), (8,0)
- Q For what values of k the following matrix isa reduced row echeleon form?[12 k2 - 4k-3][O O k 0]options:a) k = 0, 1 onlyb) k = 0, 1, 4 onlyno...
- Q For each of the following, determine if the given operation defines an inner product on the given vector space V. If it does, show that it does by verifying that...
- Q Let T: P? P? be the linear operator defined as T (p(x)) = p(3x), and let B = (1, x, x] be the standard basis for P?-Find [T]g, the matrix...
- Q Fit a linear function of the form y = co + cit to the data points (0,0), (1, 1), (2, 1) using least squares.
- Q Let A, B be (n x n)-matrices. Suppose AB = BA = In.(a) Let X, C be n m matrices.Show that AX = C if and only if X =...
- Q (ii) For n ? 3, does there exist three vectors u, v, w ? R" such that {u, v, w} is linearly dependent, and each pair {u, v}, {u, w}...
- Q Given[ 1 4 5 6 9][ 3 -2 1 4 -1 ][-1 0 -1 -2 -1][ 2 3 5 7...
- Q 2. Let G be the group defined by the following Cayley's table* 1 2 3 ...
- Q Evaluate det(det(det(det(A) A) A) A?), where A is a square matrix of order 3 with det(A) = 3.
- Q Let u, v, w be vectors in R. Which of the following statements are True? (u x v) ? (u+v) u.v x w = u x v . w lf...
- Q Find the eigenvalues of A for 1 6 2 5A=0 12 3 7 0 0 19 ...
- Q Let x, y R" be given.(a) If ||x|| = ||y|| = 1 and x * y = 1, show that x = y.(b) If ||x|| ? 1 and ||y|| ?...
- Q Given that a matrix 1 2 3A = 2 3 4 1 1 5and B=A-, find the entry in row 2...
- Q Find the eigenvalues & the eigenvectors of:A = [1 2 1 0 3 1 0 5 -1]
- Q Compute the following product of powers of matrices:You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix.[0 1 0 0 1 0...
- Q Olga buys 54 stickers. The stickers are arranged on 6 sheets, with the same number of stickers on each sheet. Which equation and answer show how many stickers are on...
- Q If E, F, G are the following elementary matrices, compute the given matrix expression.E=[1 0 0 0] F=[1 0 0 -4] G=[0 1 0 0] ...
- Q 16. Let R? have the Euclidean inner product. Find two unit vectors that are orthogonal to all three of the vectors u = (2, 1, -4,0), v = (-1,-1,2, 2),...
- Q If A is an Antisymmetric A^2 is a Symmetric and Semi define positive matrix. (Matrix B is semi define positive for each vector z matrix. Prove that -
- Q A spherical hot air balloon is about 55 feet in diameter. If air is let out at a rate of 800 feet cubed per minute, how long will it take...
- Q Consider the linear transformation T: R ? R defined by T(x, y, z) = (y, y + 2z, 3x + y ? 2z).Part(a)[3 points] Find the standard matrix of T.Part(b)[12...
- Q A Math 110 student decides to make quarterly payments of $2,500 into a retirement account paying 5% interest per year compounded continuously. If the student continues to make these payments...
- Q Suppose A is the augmented matrix of a linear system of 4 equations in 4 variables.(a) What are the dimensions of A? A is __X___(b) If the system has no...
- Q Let A be an nxn matrix and consider the linear homogeneous system Ar= 0. If the linear system has only the trivial solution state whether the following statements are true...
- Q Solve the system of equations by the addition method.-4x+y = -216x-4y = 8Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A). The...
- Q Let A be an n x n square matrix with entries in C. Suppose A is normal, show that if ? ? C is an eigenvalue of A, then |?|...
- Q (a) Determine whether the set of vectors in P? are linearly independent or linearly dependent.S=(4t-t,5+1,3t+5, 2t-31}(b) is the set Sa basis for P?? Why or why not?
- Q Let A be the matrix below and define a transformation T:R ---> R by T(u) = Au. For each of the vectors b below, find a vector u such that...
- Q Consider the system of equationsx+2y+3z=02x-y=02+kz=0.a) Calculate the determinant of the coefficient matrix using row operations.b) For which value(s) of k (if any) does the system have no solution?e) For which...
- Q Find the elementary matrix E such that EC = A where 2 4 1 2...
- Q Find a basis for the space V and determine the dimension of V.V = {(a + 3b - 2c+5d, b-c+2d, 2a+b+c+2d) : a, b, c, d ? R}
- Q Solve the following system by Gauss-Jordan elimination.2x? + 9x? + 17x?= 276x?+28X? +53x? = 83x? =x? =x?= t
- Q Write an explicit formula for the n?? term of the arithmetic sequence where the fourth term is 28 and the thirteenth term is 55.
- Q The characteristic polynomial of the matrixA=[5 -2 -4 -2 8 -2 -4 -2 5] is ?(?-9). The vector [212] is an eigenvector of A. Find an...
- Q (a) If Matrix A and B are orthogonal, determine whether the following are orthogonal or not. Give full justifications for your answer.(i) A^T, (ii) B-, (iii) B- AB.(b) Consider the...
- Q White cards are negative and graycards are positive. Find the value of the cards.9 5 3 1 7 2
- Q Use the following vectors to answer parts (a) and (b). 1 -4 3v? = -3,...
- Q The vector y has magnitude 6 and direction angle 0. The vector z has magnitude 4 and direction angle 75.Find the magnitude and direction angle ? of the sum y...
- Q Find i=3?8 (-3i)First write out the summation?Find the answer?
- Q Find the answer of the following determinant.| 1 log? y log? zlog? x 1 log? zlogz x logz y...
- Q Give the nude that describes the piecewise-defined function in the graph below.Write the rule for the function. Select the correct choice below and fill in the answer boxes to complete...
- Q Construct an orthogonal basis for the columns space of the matrix 3 5 1 1 1 0 -1 0 -2 3 ...
- Q Evaluate the limit using L'Hospital's rule if necessarylim (1 + 10/x)?/?.x??
- Q Let V be a vectors space with S = {(1, -2, 3), (2, 0, 1), (3, 0, 1), (1, 1, -1)}. Find the ff:a. Basis of RSb. dim(RS)c. Nullity (RS)
- Q Determine if the vector [5 3 0] is a linear combination of the vectors:2 1 8 -40, 4, 1, and 61 3...
- Q Let E = {x, 1}, F = {2x - 1, 2x + 1} be two ordered bases of the set of polynomials P1(x) with degree 1 or less than 1.(a)...
- Q Let A=[1 2 -2 11 3 6 -5 4 1 2 0 3](a) Find a basis for the column space...
- Q Let G = (Z??, +??) and A ? G such that A = {0, 6, 12}.1. Find all generators of G2. Find number of subgroups of G3. List all subgroups...
- Q Write an equation for a function whose graph fits the given descriptionb) The graph of f(x)=|x| is reflected through the x-axis, then shifted upwards by 4 units.
- Q We have det (A) = det(A^T) for any square matrix A. Prove this property for 2 x 2 and 3 3 matrices.
- Q Let A and B be 3x3 matrices, with det A=6 and det B=-9. Use properties of determinants to complete parts (a) through (e) below.a) Compute det AB.det AB = __________...
- Q The simple row-echelon form matrix: 1 2 0 00 0 1 00 0 0 4,shows that the system is.... of linear equations(1) an inconsistent system(2) a consistent system(3) non linear...
- Q Pick the correct statements for the given set.-1 -7 7 0-6 2Not a basis of R.Does not span R.Linearly independent.All of the...
- Q Solve the system of equations graphically. Thenclassify the system as consistent or inconsistent andthe equations as dependent or independent.4u+v=14u=v+7
- Q Consider the following system of equations.2x + y=2y-z= 4-2x + y + 2 = ?4Find the LU-factorization of the coefficient matrix.
- Q Solve the following system of equations by eliminationx + y = 84x + y = 23
- Q Find the (3, 1)-cofactor of A =1 9 -2 ...
- Q Find the standard matrix for the linear transformation T on R2 that first projects the resulting vector on y-axis then rotates the resulting vector with an angle, and then finally...
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