Matrices & Determinants Questions and Answers

2 Factor completely Then identify the roots for the quadratic function below y 2x 10x 12

1 Factor completely 3x y z 9x yz

1 point The fifth term of the sequence will be 11 1 2 5 8 True False

7 1 point Write the first four terms of a sequence given the recursive rule below f n f n 1 4 for all n 2 and f 1 32 O not enough information 32 28 24 20 32 31 30 29 O 32 27 22 17 Previous

Skew lines are a pair of lines that are non intersecting non parallel and non coplanar This implies that skew lines can never intersect and are not parallel to each other Given two lines a b c 7 40 0 0 0 0 0 L y 3 t 1 and L y 6 t 0 1 Prove that L and L are skew lines Find a vector that connects these two lines 2 6 marks 3 marks Plane lies exactly halfway between the two lines and intersects neither Use the results in Question 4 b to find the Cartesian and vector equation of plane B 16 marks

5 1 point A rectangle has perimeter P length I and width w Which of the following represents I in terms of P and w 1 P w 1 2P 2w P 2w 1 2 1 P 2w Previous

Evaluate the following expression 4 2 14 2 13 2 4 2 14 2 13 2 Simplify your answer

Tell if the quotient is zero or undefined 2 Select the correct choice below and fill in any answer boxes in yo OA 2 OB The solution is undefined OC 0 OD 2

Use the linear approximation to estimate Af f 3 1 3 for f x 1 x Use decimal notation Give your answer to three decimal places Af Estimate the actual change Use decimal notation Give your answer to six decimal places Af Compute the error and the percentage error in the linear approximation Use decimal notation Give your answer to six decimal places The error in the Linear Approximation is Use decimal notation Give your answer to two decimal places

The Commutative Property of Multiplication states that for any real numbers a and b a b 0 a b a a b b a a b b An

Evaluate the exponential expression 26 26

e Let V R Show that X w space of R x 2y 0 Go to website is a vector

valuate the following expression 11 2 6 3 1 2 6 3

Evaluate the following expression 4 1 2 17 4 17 Simplify your answer

Let B 7 1 5 32 and C 7 C 2 1 6 Find 5B 4C 5B 4C 010 000 18

1 point What is the degree of the monomial 8x y z4

Find the least squares line given the matrix products AT A ATb 1946 3 39353 8 y Ex 1 2 Ex 1 2 30 4 79 79 1617

Find the eigenvalues and eigenvectors of the following matrices using both eig and power metho for the dominant eigenvalue and eigenvector If the power method fails discuss why For those matrices that are diagonalizable give the diagonalized matrix a b 2 781344 1 921334 0 493612 1 367198 1 014289 0 015050 0 205731 0 903377 1 780261 0 824057 0 087144 0 606003 2 977860 0 140473 0 750938 0 212440 2 477599 0 980236 4 233562 1 207581 0 136646 1 168924 0 453692 0 915245 1 712964 1 54575 3 47002 1 70112 2 58917 3 28104 2 07998 1 45597 2 75629 0 55497 0 94078 2 02863 0 46100 5

Find nonzero vector in Nul A and and Cc A Find a nonzero vector in Nul A and a nonzero vector in Col A 5 231 10 1 0 2 21 1 5721

Solve the initial condition value problem x E 2 4 512 2 X x 0 1 3 C Steckch and describe the nature of the phase portrait for this system

Compare the key features of the function represented below 234 2 3 fix 3 4 x g x x intercept 1 0 1 0 2 0 y intercept 0 4 relative maximum 1 37 0 35 relative minimum 0 37 4 85 2 0 end behavior as x g x and as x g x 00

Identify the vertex the axis of symmetry the maximum or minimum value and the range of the parabola y x 2 8x 15 The vertex is

With T defined by T x Ax find a vector x whose image under T is b and determine whethe is unique 63 0 1 6 b 2 2 1 A 1

does anyone know how to make this in autocad the design is also included in the project FIGURE 5 10 10

Determine whether the data show a linear relationship If so write an equation of a line of fit Months x Hair length in y y 9 3 13 18 22 23 5 7 10 11 The data do not show a linear relationship O The data show a linear relationship The equation is y 1 75x 4 25 O The data show a linear relationship The equation is y 0 55x 2 25 O The data show a linear relationship The equation is y 2 25x 0 55 If there is a linear relationship use the selected equation to estimate y when x 15 and interpret its meaning in the context c the situation which means after months the hair will be inches in length

A T ra y Rn Let x ER a ER and A Rnxn be a real symmetric positive semidefinite matrix Let B Prove that if B0 positive semidefinite then xe Range A noting that Range A Ac for c ER I

Find the vector parametric equations for the line in the direction of the vector 7 7 5 and through the point 4 3 2 F t 1

The revenue R from the number of sales x of a certain videogame is described by the function R x 0 14x 420x

Find the dimension of the subspace spanned by the given vectors 1 2 3 5 9 4 14 7 3 11 The dimension of the subspace spanned by the given vectors is

4 2 5 2 4 2 5 2 Type Type an integer or a decimal

Perform the indicated operation 26 2 17 14 26 2 17 14

Perform the indicated operation 30 7 1 30 7 1 Type an integer or a decimal

59 The function f x 52 has an inverse function f x defined for all x 0 by which of the following expressions f x 5 2 logs x 1 A B goldfr logs x logs C D 1 1 12 x logs x 212 Smit luotol 2018

Bis 3x3 matrix with valves 2 2 where eigen 1 dim noll A 2 2 with basis ELER 11 dim Noll A 2 I 1 with basis Find the diagonalization of A ie write A POP

Find the quotient 3 35 Step by Step Solution Step 1 Write the equivalent multiplication problem 7 11 7 3 35 3 Type an integer or a fraction

Find the following quotient 4 18 4 18 25 5 25 5 Type an integer or a simplified fractie

Subtract 81 81 81 81 Simplify your answer

Find the quotient 91 56 91 56 Type an integer or a simplified fraction

Find the value of the following expression 35 147 35 147 Simplify your answer

Determine the additive inverse of the real number 5 72 The additive inverse of 5 72 is Type an integer or a decimal

Find the distance between the points Give an exact answer and an approximation to three decimal places 5 4 and 8 7 The exact distance is Simplify your answer Type an exact answer using radicals as neede

Use the Laws of Logarithms to rewrite the expression below in a form with no logarithm of a product quotient or power log4 x x 9

1 25 points Let A B 0 b 1 1 2 a Use the Cramer s rule to find the solution to Ax b b Use the Gaussian elimination to find the solution to Ax b c Give the LU decomposition of A d Use the inverse of A to find the solution to Ax b e Let B 2 3 Give the eigenvalue decomposition of B diagonalization

Replace the with the correct symbol 6 11 5 7

Fill in the blank Real numbers that can be represented with a terminating or repeating decimal are called

Round the decimal to the given place value 0 2715 nearest tenth pun 2715 round

K Rewrite the fraction 3 3 with 24 as the denominator 4

12 Let A 1 Find a diagonal matrix D and an invertible matrix P such that A P DP 2 Use the factorization A P DP to compute the power matrix A where k represents an arbitra positive integer

1 point A health research fund drive has raised 18 700 That is 22 of the goal What is the goal 1 914 187 000 85 000 411 400

Suppose that X N 1 2 X N 4 3 and Cov X X 1 Let and X X X In a matrix form find 7 A Y 14 Y 2 1 Y AX a the mean of Y b the variance covariance matrix of Y Show your working c obtain the eigenvalues and eigenvectors for Cy the variance covarian matrix of Y Show your working d hence using your answer to c show your working illustrating the va lidity of Singular Value Decomposition SVD for Car