# Matrices & Determinants Questions and Answers

Algebra
Matrices & Determinants
Perform the indicated operation 1 2 5 3 4 8 X 0 10 14 6
Algebra
Matrices & Determinants
Find 2A if A 2 7 3 1 5
Algebra
Matrices & Determinants
Use row reduction to solve the linear system X1 2x2 3x3 6 2x1 3x2 2x3 14 6x1 2x22x3 2
Algebra
Matrices & Determinants
Kiran and Mai are trying to figure out if this equation is an identity a b 4 a 4a b 6a b 4ab b Kiran picks several different values for a and b to test For each pair he tries the left side and the right side have the same value Since his tests all worked Kiran thinks the equation is an identity Who do you think had a better argument for why the equation is an identity Explain Mai started by using the distributive property the expression on the left side She then arranged the result to look the same a the right side Since she can write both sides the same way Mai thinks the equation is an identit
Algebra
Matrices & Determinants
Find all integer a such that 2 37 mod 7 20 pts
Algebra
Matrices & Determinants
7 Solve algebraically for x 3600 1 02x 2000 1 04x
Algebra
Matrices & Determinants
10 2 2 2 2 2 marks True or false If true prove it and if false give a counter example i The vector n 2 3 is perpendicular to the line 2x 3y 7 ii The set W A E Man det A 0 is a subspace of the vector space Mnn the set of all n x n matrices with the usual addition and scalar multiplication iii If E and E2 are elementary matrices then the product E E2 is an elementary matrix iy If A is an invertible symmetric matrix then adj A is also a symmetric matrix v The zero vector of any vector space is unique
Algebra
Matrices & Determinants
18 points Let be the vector space of polynomials of degree 2 or less Consider the following two ordered bases of 2 x x 2 2x x 1 x 2 x x 2 x 5 x 2x id a Find the change of basis matrix from the basis to the basis id b Find the change of basis matrix from the basis to the basis
Algebra
Matrices & Determinants
Let W be the set of all vectors 8 x y x y with x and y real Find a basis of W
Algebra
Matrices & Determinants
1 2 l 1 3 3 1 3 marks Consider the system of equations k x y z w 2x 3y 4z w 10 3x 4y 5z 2w 14 2x 5y lw For which values of k and I does the system have i no solution ii a unique solution iii exactly two solutions iv infinitely many solutions K 10 14 3 2R Rz 3R R3 2 R R4 09 D 1 03 I N N H 3 2 www 3 2 1 fund e 2 10 2k 14 3k 3 2 k
Algebra
Matrices & Determinants
How does the graph of f x x 2 4 6 compare to the parent function g x x
Algebra
Matrices & Determinants
a Solve the equation 4x 1 6 1 Show work
Algebra
Matrices & Determinants
or the function f x x 4x 45 solve f x 20 elect one a All real numbers b 9 5 Oc No solution Od 9 5 00
Algebra
Matrices & Determinants
Express the following invertible matrix A as a product of elementary matrices You can resize a matrix when appropriate by clicking and dragging the bottom right corner of the matrix A 0 2 1 2 Number of Matrices 1 Jagal
Algebra
Matrices & Determinants
1 point Find the missing coordinates such that the three vectors form an Orthonormal basis for R 0 6 0 8 1 0 6
Algebra
Matrices & Determinants
2x 5y z 8 b x 2y 3z 13 x 3y z 5 B
Algebra
Matrices & Determinants
Compute an SVD of the matrix A 34 12 6 8 6 8 2 36 36 2 8 6 8 6 12 34 What is an SVD of the matrix UEVT Round to two decimal places as needed
Algebra
Matrices & Determinants
1 Let w be a vector with initial point 4 4 and terminal point 2 5 Write w as a linear combination of the standard unit vectors i and Ow 6i 9j Ow 8i 3j Ow 0i 3j Ow i 6j w 2i 9j
Algebra
Matrices & Determinants
Find the domain and range of the relation and determine whether it is a function What is the domain of the relation OA 1 x 0 OB 1 x 1 OC 6 x 6 3 G E
Algebra
Matrices & Determinants
5 Describe the behavior of the function below as x approaches f x 3 cotx Of 1 as x O f as x Of 1 as x 1 O f 0 as x n O f o as x
Algebra
Matrices & Determinants
17 4 4 25 17 4 Ston 17 4 At least one of the answers above is NOT correct Step 1 Find the x coordinate of the vertex correct incorrect Find the vertex of y x 5x 2 using the vertex formula This problem will not accept decimal answers Please use fractions only Your answer isn t a point it looks like a real number
Algebra
Matrices & Determinants
Use the simplex method to solve the linear programming problem Minimize w 4y 2y2 subject to 3y 2y 60 4y1 y2 40 y 0 y 20 O A 80 when y 2 and y 8 OB 66 when y 0 and y 0 OC 64 when y 4 and y 24 D 48 when y 24 and y 1
Algebra
Matrices & Determinants
8 Find an algebraic expression that is equivalent to the expression tan arccos
Algebra
Matrices & Determinants
etermine the values of a for which the following system of linear equations has no solutions a unique solution or infinitely many solutions You can select always ever a or a then specify a value or comma separated list of values X1 2x2 2x3 1 3x7 6x2 9x3 12 2x7 ax2 7x3 12 Ho Solutions Unique Solution nfinitely Many Solutions Always Always Always Always Never When a SUBMIT AND MARK SAVE AND CLO
Algebra
Matrices & Determinants
58 Find an eigenpair for the matrix 2 3 5 4 2
Algebra
Matrices & Determinants
r is the growth or decay rate It is positive for growth and negative for decay Growth and decay problems can deal with money interest compounded continuously bacteria growth radioactive decay population growth etc So A t can represent any of these depending on the problem Practice The growth of a certain bacteria population can be modeled by the function A t 350e0 0796t where A t is the number of bacteria and t represents the time in minutes a What is the initial number of bacteria 350 round to the nearest whole number of bacteria b What is the number of bacteria after 20 minutes 1720 round to the nearest whole number of bacteria c How long will it take for the number of bacteria to double least 3 decimal places your answer must be accurate to at
Algebra
Matrices & Determinants
19 Find the matrix A if 2 26 10 27 41434 if 4 e 10 26 13 5 b 7 26 3 10
Algebra
Matrices & Determinants
16 Let V v2 3 and v3 Note that V V2 V3 is an orthonormal set Find ca so that C V1 C2V2 C3V3 a b c d c
Algebra
Matrices & Determinants
21 Suppose that A is a matrix with eigenvalues A 9 and 8 with corresponding and 5 respectively Find a22 i e find the entry in row 2 column 2 of eigenvectors the matrix A a 4 b 5 c 1 d 3 e 2
Algebra
Matrices & Determinants
18 Which of the following statements are always true 1 If A is a square matrix then tr A tr A ii If A and B are matrices such that AB B then A I ii If A and B are symmetric matrices of the same size then the matrix AB is also symmetric a 1 only b all of them c i and iii only d i and ii only e ii and iii only
Algebra
Matrices & Determinants
8 Which of the following sets of vectors span R2 i 1 2 1 0 ii 1 1 2 2 iii 1 0 0 1 3 4 a i only b i and iii only c iii only d all of them e i and ii
Algebra
Matrices & Determinants
10 Let V be the subset of R consisting of all vectors of the form a b c d where d a b c Find a basis for V a 1 0 0 0 0 1 0 0 0 0 1 0 b 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 c 1 1 1 3 d 1 1 1 3 1 0 1 2 e 1 0 0 1 0 1 0 1 0 0 1 1
Algebra
Matrices & Determinants
2 Find the Hill cipher of the word AT using the following enciphering matrix 3 A B C D E F G H I J K L M N O P Q R S T U V W X Y 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 a OP b BC c BR d OX e ZP
Algebra
Matrices & Determinants
Find a basis for the null space of A 80A D 0 48840 e a d 1 2 4 5 A 0 1 3 2 1 0 0 1 2 b c
Algebra
Matrices & Determinants
1 A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly From point A th biologist walks downstream x 150 feet and sights to point C see figure From this sighting it is determined that 0 54 How wide is the river 0 54 AXI
Algebra
Matrices & Determinants
Let W be the subspace spanned by u and u and write y as the sum of a vector in W and a vector orthogonal to W 7 U 1 4 3 5 The sum is y z where y is in W and z Simplif SIDD is orthogonal to W
Algebra
Matrices & Determinants
L Simplify the following expressions and express your answers with positive exponents a x x 5 d 13 8 JAL M Before we can apply the rules of exponents to expressions in the form of a n where the exponent is a fraction we need to consider what such an expression means Simplify the following expressions a x1 2 x 1 2 c m 2 m 2 9 then m d h 2 h 2 If h The expression a called a b a xxx h1 2 Simplify the following expressions 1 2 is often written as If h 5 5 6 d h 3 h 3 h1 3 1 2 c 5 5 5 5 then x h1 3 1 3 C 1 2 16 broc com what s another way to write h 23 x 2 and is called the ola 1 3 The nth Root If a is a real number and n is a positive integer a a b 41 2 41 2 what s another way to write h 32 b 1 3 27 the nth root of a e v 2 w5 v of a The symbol 8 is
Algebra
Matrices & Determinants
Solve the following system of equations If there is a unique solution enter it as an ordered pair in the form x y If there is no solution enter Inconsistent If there are infinitely many solutions enter your answer as a line in the form y mx b 2x 3y 3 6x9y 9
Algebra
Matrices & Determinants
By hand solve the system using matrices and row operations List each row operation as we have done in class i e R3 10r2 73 Give exact answers in fraction form If the system has no solution state this If the system has an infinite number of solutions give one solution x y z 8 2x 3y z 2 3x 2y9z 9
Algebra
Matrices & Determinants
6 Given a 10 b 6 and c 14 use the Law of Cosines to solve the triangle for the value of B Round your answer to two decimal places 0 60 33 0 80 44 38 21 120 00
Algebra
Matrices & Determinants
7 Use the figure below to find the exact value of the given trigonometric expression 0 sin 2 24 figura not 10 accari to sagla
Algebra
Matrices & Determinants
Rewrite the system as an augmented matrix then use your calculator to write the matrix 10 in row echelon form REF Use back substitution to solve the system Give exact answers in fraction form If the system has no solution state this If the system has an infinite number of solutions give one solution x 5y z 1 3x 11y4z 1 3x 10y 7z 5
Algebra
Matrices & Determinants
3 Evaluate the following expression 4 O 0 4 3 sec y 3 cot 7 y 2 3 3
Algebra
Matrices & Determinants
Find the eigenvalues of the symmetric matrix Enter your answers as a comma separated list Enter your answers from smallest to largest 044 404 444 A1 For each eigenvalue find the dimension of the corresponding eigenspace Enter your answers as a comma separated list dim x
Algebra
Matrices & Determinants
Let f x 3x 4 What is the domain of f x What is the range of f x Determine f x f x What is the domain of f x What is the range of f x
Algebra
Matrices & Determinants
The expenses and income of an individual are given in table form to the right Find the net monthly cash flow it may be negative or positive Assume that amounts shown for salaries and wages are after taxes and that 1 month 4 weeks Income Part time job 1100 month Student loans 8400 year Scholarship 6500 year The net monthly cash flow is Round to the nearest dollar as needed Rent 550 month Expenses Groceries 50 week Tuition and fees 6500 year Health insurance 25 month Entertainment 100 month Phone 65 month
Algebra
Matrices & Determinants
16 14 The solution is 7
Algebra
Matrices & Determinants
Click here to watch the video 17x 9 Find the quotient 3 cis 17x 9 3 cis 9 cis 2x 9 in rectangular form using exact values 2x 9 cis 9 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi
Algebra
Matrices & Determinants
6 From a point 125 m from the foot of a building the angles of elev the building s flagpole are 40 and 38 respectively 380 409 125 m Calculate a the height of the building the Height of the building is 236 66m Tall Pe 125 38 125 x x 138 125 125 7 125 78m T H 164 88 125 78 b the length of the flagpole 230 66 104 88 O X x Tanus Tan 88 125 78 x 104 88m 125 Tan 38 buo a Tan38 125 78 Tan 40 X Tan Uc
Algebra
Matrices & Determinants
A garden is in the shape of a rectangle 43 feet long and 13 feet wide If fencing costs 6 25 a foot what will it cost to place fencing around the garden 118 25 3 493 75 350 00 700 00