Matrices & Determinants Questions and Answers

er 5 6 Mastery Quiz Determine whether the given ordered pair is a solution of the system 1 4 3x 2y 5 2x 5y 29 O solution Question 10 o not a solution

1 point company sells bottles of vitamin capsules The rdered

Miguel 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

For 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

Consider 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

uppose 2 1 1 Then 3 1 5 1 5 is 4 2 2 is 3 3 2 is

Use 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

Assume A is a 3 x 3 matrix and A 2 A A 0 0 2 6 Then an eigenvalue for A is

7 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

Let 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

Systematic 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

b Solve the difference equation Yt 1 2y 12t

Use 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

2 Determine the direction angles to the nearest degree for the vector a 6 2 3 3

1 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

Consider 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

A 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

Below 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

8 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

Question 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

4 Let A Find two different diagonal matrices D and the corresponding matrix S such that A SDS 1981 188

1 point The system 8z 8y 17 z 71 19 z Sy 3z 3y has the solution z 1 2 6z 1 y Z

15 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

2 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

em 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

he 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

entence based on the equation shown h 2x 10 14 x 6

The 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

Question 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

Let 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

Graph 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

If f x 5x 5 and g x x 6 find fog x and gof x fog x gof x

6 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

p 9 3 2 8 5 76 In the picture given that m 4 83 degrees m28 must be type your answer degre

the following system of equations using Cram 3y 15x 24x A 24y 20

Question 13 12 4u 4v 4w e of x 28 y 20 z 8 if it is

system 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

Sketch the graph of f x 4 4 Describe how the graph can be obtained from the graph of a basic exponential function

se the properties of logarithms se a graphing calculator to eva

inverse matrix and matrix multiplicat 1x 60y 9z 27

of 11 43 1 4 1 4 y z 1 3y z 4 is 517 F 87 337 I 417 517 111 Use it

Which matrix equation represents the system of equations y 2 3x 2y 0

Question 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

nd 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

4 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

hverse of 1 1 1 0 2 1 is 4 5 x y z C 2y z 1 0 5 5 1 4 1 4 8 9 2

Find 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

2 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

An 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

Theorem 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