Algebra question and answers for August 13, 2023
- Q Find the values of the variables in the equation 1 X y Z 8 3 3 7 8 x y z
- Q Suppose A 1 mark 1 A 1 1 A A 0 196 0 1 1 020 0 01 0 02 A 1 0 00 1 1 1 1 1 0...
- Q Question No 2 For which real values of a do the polynomials P t at t P t at pa t t t a form basis for vector space P
- Q A is a 2x2 matrix You are told that 4 3 3 and A 3 2 3 Then the general solution of y Ay is O C e t C...
- Q Find a formula for A using the technique covered in class You may use Maple to comput the eigenvalues and eigenvectors of A You must show everything else A 7...
- Q State if each pair of triangles are similar If by which method 1 2 H S 48 N241 ALMN R 77 84 63 9 A F G H G J...
- Q 23 For each of the following matrices find an invertible matrix P and a diagonal matrix D such that A PDP a A b A 1 2 3 4 2...
- Q 8 Solve the inequality 5 x x 1 AI
- Q Let A 5 2 2 1 22 4 a Find all eigenvalues of A over R b For each of the eigenvalues you found under a find the corresponding eige
- Q Exercice 3 Let A Compute R A 21 1 3 0 4 1 42 4 4 1 5 5 2 1 3 1 0 4 3 634 8 1 9...
- Q 0 C Let S 1 mark Which of the following statement is true S is orthogonal but cannot be normalized to an orthonormal set S is not orthogonal S can...
- Q Exercice 9 Let A 0 1 1 1 0 1 1 1 0 1 10 and B 0 001 000 1 Judge if A could be similar to a diagonal...
- Q For the matrix A Select one 1 we have 1 True O False AT A 1 9 2
- Q 0 0 0 0 0 0 S2 4 O 2 5 72 S3 1 mark Drag the options on the left and drop them into the options on the right...
- Q Suppose a four sector economy presents the following internal consumption matrix A and external demand vector d A 0 100 0 0 50 0 0 010 0 0 020 0...
- Q 2 Let A 1 2 1 1 1 302 2 0 1 1 3 1 2 5 13 2243 5 a Find N A with it basis b Find the...
- Q A few steps in the process of simplifying the given matrix to row echelon form with 1s down the diagonal from upper left to lower right and Os below the...
- Q Exercice 1 Let 1 1 Find A4 2 Find A for n 5 A 0 1 0 0 0 00100 00010 0 0 0 0 1 00000
- Q Suppose A and B are square matrices of the same size Which of the following are NOT necessarily true AB A B A B A B A B A B...
- Q 4 14 5 Given A 6 14 4 observe that the first column plus twice the third column equals the second column Find a nontrivial solution of Ax 0 without...
- Q Given the following matrices A and B find an invertible matrix UI such that UA You can resize a matrix when appropriate by clicking and dragging the bottom right corner...
- Q 13 53 Construct a 2 x 2 matrix C such that AB AC but C B Consider the matrices A C 1 3 O no O yes and B There...
- Q and the value s of h for which the vectors are linearly dependent Justify your answer 1380 7 The value s of h which makes the vectors linearly dependent is...
- Q 4 points a 15 points Can B find scalars 2 such that B A A be written as a linear combination of A 6 and A 1 If so
- Q Orthogonal Projection II ind orthogonal projection of the vector 7 X nto the subspace Answer W span 3 0 9 Your response 31 18 5 9 1 18 Correc
- Q A 1 1 0 2 13 1 1 0 2 1 3 2 2 1 0 1 7 2 1 a Find a row reduced echelon matrix R which is...
- Q The 4x4 matrix uses excel 1 2 3 4 1 10 5 2 11 4 3 15 5 4 20 1 det A 1 4224 solve A 1 4 6...
- Q 3 11 B B 2 0 2 Show whether this list of three vectors is linearly independent or linearly dependent 2 5 points Given a list of three vectors V...
- Q Find the geometric and algebraic multiplicity of each eigenvalue and determine whether A is diagonalizable If so find a matrix P that diagonalizes A and determine P AP Notice that...
- Q Use the method of Example 6 to compute the matrix A 0 where 1 2 A 1 2 2 i 2048
- Q Recall that R m n denotes the set of all m x n matrices with real number entries How many of the following assertions are correct 2 4p Recall that...
- Q 3 Find the matrix of the transformations T R2 R2 in the basis B 2 a T is reflection with respect to the line ya b T is projection onto...
- Q Let u and v be two vectors such that If u k 1 1 1 then k 12 48 12 144 4 u 12 v 3 compvu 4 and projuv
- Q A 2 1 1 1 Does A has a one sided inverse If yes find at least two different ones 1
- Q Tute eigenvalues and bases for the eigenspaces of AP for O A 1024 A 1024 GIGIFI CAH O A 1024 0 4 O A 1024 A 4 EG A 4...
- Q 1 estion 1 6 points Let A 2 i i 2 i 7 4i 28 i 10 12i a Show that A is positive definite by using principal submatrices of...
- Q 2 2 3 A 2 32 4 25 Eigen value and basis basis for eigen space by A 3 1 1 A 10 1 1 1 E All False 2...
- Q Question 2 4 points Find a QR factorization of A 2 2
- Q Problem Let A 8 7 points 11 1 2 22 3 1 1 10 5 A 2 G G 6 0 G C 3 D 2 5 G B 1...
- Q Find a basis for S AE M x2 the sum of the entries of A is f A is 0
- Q Problem 5 7 points Find the coordinate vector v where v 3 x 62 and 8 1 2 2 2 2x x A 3 1 6 B 1 3 6...
- Q 2 Let M be the magic 6 x 6 matrix Determine the matrix U2 I where U is the upper triangular matrix in the LU decomposition of M
- Q 5 Use the table below to predict how long it would take to walk 40 6 miles Round your answer to the nearest hundredth Time Miles 0 4 95 9...
- Q Simple linear regression Explained and unexplained variation Bivariate data obtained for the paired variables x and y are shown below in the table labeled Sample data These data are plotted...
- Q the system of equations corresponding to the augmented matrix Then perform the row operations R 4r2 and R3 2r2 r3 on the given augmented matrix 9 4 1 5 2...
- Q In Exercises 13 14 find proj u 13 a u 1 2 a 4 3 b u 3 0 4 a 2 3 3 14 a u 5 6 a...
- Q Suppose A has eigenvalues 3 1 with corresponding eigenvectors u U EASANT Find the following Express your answer in terms of us and 2 enter u as u 1 and...
- Q y 2x 14 are O 5 24 4 22 O 8 30 4 6 O 5 4 4 22 O 8 24 4 6 Write and solve the equation based...
- Q Question 1 Evaluate the determinant of the matrix using theorem 3 6 40 25 10 A 30 5 20 15 35 45
- Q A pine tree growing on a hillside makes a 77 angle with the hill From a point 82 feet up the hill the angle of elevation to the top of...
- Q 4 If x 5 y 3 and z 12 calculate the following EZ A
- Q 12 Let x 1 y 4 and z 4 Evaluate 4x 6 1z 2y
- Q Solve the given system of differential equations by systematic elimination Dx y Dy z Dz x x t y t z t
- Q Use row reduction to evaluate the determinant of the matrix Do not use cofactors 3 0 2 6 9 0 2 1 5
- Q Find the volume between the cone x y z and the sphere x y z 25
- Q 7 Is matrix A 2 diagonalizable A If yes diagonalize it then find A
- Q 9 What is the cosine of angle between matrices A and B with respect to standard inner product on M22 1 31 A 2 21 B 23 1
- Q 10 Is S V1 V2 V33 where v 2 1 0 v 1 2 0 and v 0 0 1 an orthogonal set with respect to the Euclidean inner product...
- Q 6 Find the bases for the row space column space and null space of the following matrix then find A 4 51 A 3 2 2 1 10 8
- Q Suppose the production of 1 unit of mining requires 2 5 unit of mining 1 10 unit of manufacturing and 1 2 unit of communication To produce 1 unit of...
- Q The profit function P is shown for producing and selling x items Determine the values of x for which a P x 0 the company breaks even b P x...
- Q C x 35 8x 3776 Part 2 of 4 b Write a linear revenue function that represents the revenue R x for selling x items The linear revenue function is...
- Q Compute the product AB by the definition of the product of matrices where Ab and Ab are computed separately and by the row column rule for computing AB 1 3...
- Q Find the values of x and y using pseudoinverse X 3y 5x 7y 11x 13y 17 19 23 P aa Ta P A ATA 1AT A
- Q 4 In the triangle below 5 represents which ratio A 3 C O sinc OsinB OcosC tanB 4 5 B
- Q One leg of a right triangle measures 6 inches The remaining leg measures 63 inches What is the measure of the angle opposite the leg that is 6 inches long...
- Q Which graph best represents the solution of the inequality y22 x 11 27 SA ty Select one OA OB OC OD ty of 2 O
- Q Find the inverse of the affine transformation F x 2 x 2
- Q Find F dr for the given F and C 7 y7 x 3k and C is the helix x cos t y sin t z t for 0 t 3x...
- Q 10 points 8 a Let A 1 3 27 31 1 24 Find a basis for ColA
- Q 77 points 10 The matrix A 8 1 2 is symmetric and therefore orthogonally diagonalizable The characteristic equation of A is 2 5 2 16 0 Find an orthogonal matrix...
- Q m 1 m 2 2 n Given two 3 matrices A 1 and E 1 1 11 2 1 0 values of m and n such that A E has...
- Q Find the solution set of the system of linear equations represented by the augmented matrix If there is no solution enter NO SOLUTION the system has an infinite number of...
- Q 2 pts Calculate the characteristic values and characteristic vectors of the following matrix and verify that it is equal to the determinant 3 4 21 A 0 1 2
- Q 0 0 0 0 0 Ix 11 12 OTO 0 1 1 0 0 0
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