Matrices & Determinants Questions and Answers
Algebra
Matrices & DeterminantsMiguel invests 10000 in two different accounts The first account paid 14 the second account paid 8 in interest At the end of the first year he had earned 1118 in interest How much was in each account
Algebra
Matrices & DeterminantsFor non null matrices A and B of the same order which of the following statements is true A A B B A B AB B A A B C II B A D None of them
Algebra
Matrices & DeterminantsConsider the inner product on R defined by u v u Av for some 2 x 2 positive definite matrix A Determine A if of 11 Then A IT 7 and H 4 1
Algebra
Matrices & DeterminantsUse the figure below which shows the unit circle with increments of 0 1 units marked off along the circumference in a counterclockwise direction starting from 1 Estimate 8 if cos 8 0 2 and 0 6 2m Enter your answers as a comma separated list Round your answers to one decimal place 8 3 rad 3 0 8 TTTT 2 0 4 0 8 0 4 0 0 4 0 8 0 4 0 8 HTTTT 6
Algebra
Matrices & DeterminantsAssume A is a 3 x 3 matrix and A 2 A A 0 0 2 6 Then an eigenvalue for A is
Algebra
Matrices & Determinants7 f x 9 Jos x 5X 6 x 4x 3 x 2 x 3 x 3 x 1 none 3 X 2 0 X 2 12 0 X 3 0 X 3 none x 41 0 8 M X X 3 0 X 3 13 0 X 1 0 x 1 19 0 06 3X
Algebra
Matrices & DeterminantsLet W be the subspace of R4 spanned by the vectors Find the matrix A of the orthogonal projection onto W A and 8 1 7
Algebra
Matrices & DeterminantsSystematic Sampling Convenience Sampling Question 5 14 3 points What type of data set would best describe the following list A list of each students GPA for a graduating class to determine the valedictorian Qualitative Quantitative Neither
Algebra
Matrices & DeterminantsUse an inverse matrix to find x for the given x and B 5 6 4 HA B 3 X B Simplify your answer 8 6
Algebra
Matrices & Determinants2 Determine the direction angles to the nearest degree for the vector a 6 2 3 3
Algebra
Matrices & Determinants1 pt Let A 1 5 9 5 5 5 S Find Sl and Disuch that A SDS 1 1 1 9 5 0 0 D 0 0 0 0
Algebra
Matrices & DeterminantsConsider the function 2 X2 Y 90 Y3 58 X2 76 Y2 47 X 27 Find the Hessian matrix associated with this function ab sin a f di 8 R S2 111
Algebra
Matrices & DeterminantsA is a 3 x 3 matrix with eigenvectors v Write x as a linear combination of the given eigenvectors x Find A20x and M A v corresponding to eigenvalues 22 and 23 1 respectively and x 8 9
Algebra
Matrices & DeterminantsBelow is the graph of f x x 6x 9 with a restricted domain Which is true of the inverse of the function AY al 10 N 8 7 6 5 4 3 2 1 OL 2 246 6 8 10 2 X The inverse has a domain that includes all values of x greater than or equal to 0 O The inverse has a range that includes all values of y greater than or equal to 0 The inverse is a function O The function has a domain that includes all values of x greater than or equal to 0
Algebra
Matrices & Determinants8 For each of the following matrices determine the value s of c for which the given matrix is not invertible 1 2 a 0 1 13 4 b 2 2 4 3 5 1 C C 7
Algebra
Matrices & DeterminantsQuestion 3 of 8 1 poi Graph the function and writ g x 6 Part 0 2 Part 1 of 2 Graph the function g x
Algebra
Matrices & Determinants4 Let A Find two different diagonal matrices D and the corresponding matrix S such that A SDS 1981 188
Algebra
Matrices & Determinants1 point The system 8z 8y 17 z 71 19 z Sy 3z 3y has the solution z 1 2 6z 1 y Z
Algebra
Matrices & Determinants15 points If A and B are 4 x 4 matrices det A 4 det B 8 then det AB det 2A det AT det B det B4
Algebra
Matrices & Determinants2 Consider the following system of linear algebraic equations x 4x 2x 3 4x 2x x 1 2x 2x 5x 3 Does the given system has a unique solution If yes find this unique solution by using LU decomposition method
Algebra
Matrices & Determinantsem 10 Let oblem 10 a A T 4 2 5 1 6 16 2 1 1 3 3 a Find the dimension of the row space of A b Find the dimension of the nullspace of A
Algebra
Matrices & Determinantshe eigenvalues of the coefficient matrix can be found by inspection or factoring Apply the eigenvalue method to find a general soluti of the system x 4x 2x 2x3 x2 7x 5x 2x3 x3 7x 7x 4x3 What is the general solution in matrix form CITE
Algebra
Matrices & DeterminantsThe zeros in the given matrix make its characteristic polynomial easy to calculate Find the general solution of x Ax 0 0 0 21 5 27 9 00 5 0 0 0 21 2 A 2 COD
Algebra
Matrices & DeterminantsQuestion 21 of 21 Rudd Clothiers is a small company that manufactures tall men s suits The company has used a standard cost accounting system May 2020 10 500 suits were produced The following standard and actual cost data applied to the month of May when normal capacity was 13 000 direct labor hours All materials purchased were used Cost Element Direct materials Direct labor Overhead 2 1 2 7 yards at 4 00 per yard b 1 10 hours at 13 00 per hour 1 10 hours at 6 40 per hour fixed 3 60 variable 2 80 Overhead is applied on the basis of direct labor hours At normal capacity budgeted fixed overhead costs were 46 800 and budgeted variable overhead was 36 400 Total materials variance Compute the total price and quantity variances for 1 materials and 2 labor Round per unit values to 2 decimal places eg 52 75 and final answers to 0 decimal places eg 52 Materials price variance Materials quantity variance Standard per unit Total labor variance Labor price variance Labor quantity variance Compute the total overhead variance S S S S 15 Actual S S 281 580 for 74 100 yards 3 80 per yard 162 810 for 12 150 hours 13 40 per hour 49 400 fixed overhead 37 500 variable overhead
Algebra
Matrices & DeterminantsLet P 0 5 0 9 0 5 0 1 Computex and X x2 be the transition matrix for a Markov chain with two states Let xo 0 5 0 5 be the initial state vector for the population
Algebra
Matrices & DeterminantsGraph the function f x 2 2 by moving the key points and the horizontal asymptote as needed Provide your answer below S 50 0 5
Algebra
Matrices & Determinants6 1 point Scalene Triangle 1 point B If the measure of angle A is 95 degrees and the measure of angle C is 30 degrees what must be the measure of angle B The measure of angle B is type your answer degrees Scalene Triangle B W MATH MONKS Gamalo MATH Mans If the measure of angle B is 45 degrees and the measure of angle C is 27 degrees what must be the measure of angle A nswer degrees
Algebra
Matrices & Determinantsp 9 3 2 8 5 76 In the picture given that m 4 83 degrees m28 must be type your answer degre
Algebra
Matrices & Determinantssystem of equations using Cramer s Rule if it 3y z 3 1 6y z 0 2 3y 5z 1 3 correct choice below and fill in any answer I
Algebra
Matrices & DeterminantsSketch the graph of f x 4 4 Describe how the graph can be obtained from the graph of a basic exponential function
Algebra
Matrices & DeterminantsQuestion 4 Worldwide annual sales of a device in 2012 2013 were approximately q 5p 4000 million units at a selling price of p per unit Assuming a manufacturing cost of 75 per unit a Find the profit function b What selling price will give the greatest profit c What would be the resulting profit
Algebra
Matrices & Determinantsnd an invertible matrix P and a diagonal matrix D such that P AP D 13 12 12 1 10 9 12 0 0 3 P 000 C 000
Algebra
Matrices & Determinants4 A piece of wire L m long is cut into two pieces One piece is bent into a square and the other is bent into an equilateral triangle How should the wire be cut so that the total enclosed area is a a maximum b A minimum
Algebra
Matrices & DeterminantsFind the inverse of the given nonsingular matrix 1 1 02 1 320 1 1 The inverse of the matrix 0 3 2 1 is 20
Algebra
Matrices & Determinants2 Let V R and define a function VxV R by 2 1 0 2 110 0 1 2 v w v a Verify that the given function is an inner product on V b Starting with the standard basis of V use the Gram Schmidt process to find an orthonormal basis of V c Leto V R be the linear functional defined by Use the Reisz Representation Theorem to a vector u R such that o a 2 1 1 1 3x3
Algebra
Matrices & DeterminantsAn important aspect of computer graphics is the ability to transform the coordinates of points within an image For transformation purposes a point x y is represented as the column X matrix X To rotate a point multiply a point s column matrix by an appropriate rotation matrix R to form the matrix product RX For example to rotate a point by 45 in the counterclockwise direction the rotation matrix is to the right Use this information to answer parts a and b below R 2 2 2 2 2 2 2 01 MAN a Write the coordinates of the point 8 10 after it has been rotated by 45 in the counterclockwise direction Type an ordered pair Type an exact answer using radicals as needed Use integers or fractions for any numbers in the exp
Algebra
Matrices & DeterminantsTheorem If A is an algebra of subsets of X and A E A i 1 2 then 3B CX such that B A i 1 2 and B being pairwise disjoint with UB UA Proof HW3
Algebra
Matrices & DeterminantsLevi want so make a square patio in his yard He has enough concrete to pave an area of 140 square feet If A represents the area of the patio and s represents the side length of the patio use the formula s A to find the length of each side of his patio Round your answer to the nearest tenth of a foot Answer