Matrices & Determinants Questions and Answers

Given the equation of the sphere x 2 y 3 z 1 2 What are the equations of the planes that are tangent to the sphere and parallel to the xz plane

out bobuled toward a dock as shown in the figure to the right if the rope is being pulled in at the rate of 4 feet per second how fast is the distance tiveren the dock and the boat decreasing when it is 3 feet from the dock the distance between the dock and the boat is decreasing by 6 667 feet per second when the boat is 3 feet from the dock Round to the nearest thousandth as needed Sivat Roge

4 points Find values of b and d so that the matrix 1 b 1 d that will change the point 2 5 into the point 8 17 when you multiply 1 b 1 d 2 5 Show your work

Simplify 45mn 20n Rubric 1 point for the work shown 1 point for the correct answer

Find all the possible values of tan Select one or more 25 4 a b C d e f 17 4 3 4 21 4 5 11 4

Find the quotient using synthetic division Express the quotient as a rational expression 3 1 3 10 12

Find the Fourier series of the given function below 2 x 0 a f x x 0 x 1 1 x 2

For the following verify that the subset D of the group G is a difference set and determine the value of X a D 0 1 2 4 5 8 10 and G Z15 b D 0 1 0 2 0 3 1 0 2 0 3 0 and G Z4 x Z4 Recall that Z4 X Z is the group whose elements are ordered pairs of elements of Z with the operation being componentwise

mework Question 3 2 Part 1 of 5 Determine the largest open intervals of the domain function is a increasing b decreasing and c c the d domain and e range Over what open interval s if any is the functio Select the correct choice below and if necessary box to complete your choice A The function is increasing on the open inte

ork Question e given graph to solve the following inequa 20 olution set for y y 20 is answer in interval notation

valuate the indefinite integral 0 c C tegral p 330000 ELOT J cos x cos 3 sin x dx

Use the contour diagram off in the figure below to find the approximate direction of the gradient vector at the point 2 2 2 L 7 7 3 3 1 0 7 7 07 7 0 7 7 07 7 1 2 3 H OneDrive

7 x 1 f x Start by drawing the vertical and horizontal asymptotes Then plot two points on each piece of the graph Finally click on the graph a function butt 8 37 6 5 4 3 2 4 3 4 3 COO T Lini JOLL G

Oh the linear equation using the slope intercept me 11x 2y 1 e the graphing tool to graph the equation Use the na and the v internant when drawing the line

Write an equation of the line Horizontal through 0 2

Find a polynomial function of degree 3 with real co Zero of 4 having multiplicity 3 1 25

5 Suppose the value R d of d dollars in euros is given by R d d 6 The cost P n in dollars to purchase and ship n purses is given by P n 55n 23 Write a formula for the cost n in euros to purchase and ship purses It is not necessary to simplify Q n 0 X A

5 2 2 Let A be the matrix A a Find all eigenvalue and coresponding eigenvector of A b Find a matrix P such that P AP is a diagonal matrix c Use result of part b determine A2021

Show that the ith component of the vector ax bxa may be written as cb where b are th components of b Determine the form of c in terms of the components of a and show that it is symmetric object that is c c for all i Use Einstein notation

QUESTION 5 6 marks Let A be a 6 x 6 matrix such that the sum of all the odd numbered columns of A is equal to the sum of all the even numbered columns of A Show that A 24 342 4A 51 0

Find the characteristic equation for the matrix below and determine its eigenvalues and ne corresponding eigenvectors 1 3 1 2 A 3 0 2 1

Using the matrix equation E AM as well as the key and encoding matrix below A 1 B 2 14 N O P C 3 15 16 D 4 Q 17 E 5 R 18 F 6 S 19 G H 7 8 T U 20 21 r1 21 I J 9 10 V 22 K 11 23 W X Y L 12 24 25 M 13 N 26

Determine the value s of h such that the matrix is the augmented matrix of a consistent linear system 20 28 h 5 7 1 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The matrix is the augmented matrix of a consistent linear system if h Use a comma to separate answers as needed Type an integer or a simplified fraction B The matrix is the augmented matrix of a consistent linear system if h OC Use a comma to separate answers as needed Type an integer or a simplified fraction The matrix is the augmented matrix of a consistent linear system for every value of h For any value of h O D The matrix is not the augmented matrix of a consistent linear system

apply Theorem 5 to find the inverse A 1 of each matrix A 3 2 5 530 2 4 5

Help Entering Answers 1 point Identify the surfaces with the given vector equations hyperbolic paraboloid elliptical paraboloid plane hyperboloid of one sheet describes r u v 3u 4v u v describes r u v sin u 3v 3 cos u describes r s t describes r s t t sin 3s i 4t j t cos 3s k 4si 3t s 4 j tk

Determine whether the following matrices are in echelon form reduced echelon form or not in echelon form a Not in Echelon Form b Not in Echelon Form c Reduced Echelon Form Not in Echelon Form 10 0 1 0 30 1 1 1 7 100 5 0 0 0 0 010 3 100

In triangle ABC measure of angle ABC 150 AB 3v3 and BC 4 The line through A that is perpendicular to AB and the line through C that is perpendicular to BC meet at D Find the area of quadrilateral ABCD

The matrix has three distinct real eigenvalues if and only if k A 14 k 1 01 4 1 0 0

Show that T is a linear transformation by finding a matrix that implements the mapping Note that x X are not vectors but are entries in vectors T X X2 X3 x 7X 8X3 X2 4X3 A COLES Type an integer or decimal for each matrix element

For the function f x x2 5 construct and simplify the difference quotient f x h f x h

3 Find all value s of k that make the following system of equations 3x 2y 10 6x 4y k have a a unique solution b infinitely many solutions c no solution For each case explain your answer for example with a geometric interpretation It may be possible that no such k exists in other words that case cannot occur If that happens explain why

pint If 9 5 A 3 6 5 A 4B and B 9 9 8 11

Find all possible functions with the given derivative f x x TAVA

Solve for the unknowns in the vector equation below 2 b D M N N 1 9 4 3 3 b a a 9

Let A 5 20 16 4 olumns for B Construct a 2x2 matrix B such that AB is the zero matrix Use two different nonzer

Determine if the function f x x is differentiable at x 0 If not identify why a f x x is not differentiable at x 0 because f 0 is not defined b f x x is differentiable at x 0 c f x x is not differentiable at x 0 because f 0 is not defined d f x x is not differentiable at x 0 because lim x does not exist x 0

11 2m n 12 m 2n 9

Solve the following system of linear equations x 3y z 1 2xy 2z 3 5x 8y a 10 z a 3

Hading Feb 10 8 09 48 AM Subtract x 6x from 5x2 7x 10

Suppose some surface is described by the parameterization p u v 2u 3v u v Find two nonparallel vectors which are tangent to this surface at the point 4 3 5

The figure shows the rectangle ABCD where AB 80 cm and AD 60 cm Let E F and be points lying on AD AB and BC respectively such that DE AF 48 cm and CG 30 Denote the point of intersection of DF and EG by H Find BH correct to the nearest 0 1 cm A 37 4 cm B 37 5 cm C 51 2 cm D 51 3 cm A E D H F

Complete the eigenvalues and eigenvectors of A Enter eigenvalues in the order a bi a bi Eigenvalue A Ex 5 71 Eigenvector x Eigenvalue A Eigenvector x H 1 1 8 3 1 1

2 Consider the matrix equation 2 0 4 MT 2 0 2 3 1 2 Find the matrix M that satisfies this matrix equation T 8 2 3 3 C 0 1 1

pint Let A be a 3 x 2 matrix and suppose we know that u r 1 and v satisfy the equations Au a and Av b Find a solution x to Ax 3a 2b

1 point A linear transformation T R R whose matrix is 3 9 2 6 is onto if and only if k 22 5 9 4 5 0 5 k

low is an aumented matrix of a sys ny solutions Try to perform as few B 1 0 0 3 4 0 1 3 1 1 0 0 1 1 0

Find the measure of the each angle to the nearest degree s 1 10 13 cos

Find an equation of the plane that is passing through the points A 5 1 3 and B 2 2 1 and is perpendicular to the plane 2x y z 4 Sketch its graph

Find a QR factorization of the matrix 10 0 1 21 1 0 1 2 2 1

1 point If T R R2 is a linear transformation such that then the standard matrix of Tis A T 25 and 7 13 T 8