Matrices & Determinants Questions and Answers
Algebra
Matrices & Determinants5 Find a basis for the solution space of the following homogeneous linear system and find the dimension of that space 3x1 x2 x3 X4 0 5x1 X2 X3 X4 0
Algebra
Matrices & Determinants1 Are the following sets of vectors linearly independent Why a u 2 3 and u 1 2 and 3 3 1 in R b p 1 2x x and P 2 4x 2 x in P2 c A 1 03 05 in M 2 and B
Algebra
Matrices & Determinants6 Find the basis for the given subspaces of R and state the dimension a 2x 3y 4z 0 b 2x 3y 0
Algebra
Matrices & DeterminantsIn planning her retirement Liza deposits some money at 2 interest with twice as much deposited at 2 5 Find the amount deposited at each rate if the total annual interest income is 700 She deposited at 2 and at 2 5
Algebra
Matrices & DeterminantsFind the slope of the secant to the curve f x x 5 between x 2 and x 1 O a 3 b 1 3 c 3 d Submitting Your Test
Algebra
Matrices & DeterminantsDetermine the composite function fog and gof For each composite function state the domain and range a f x 5 2x x and g x 1 6x b f x 3 and g x log x c f x sin x and g x 4x 6x 2 d f x 4x 1 and g x x
Algebra
Matrices & Determinantse differential equation y ay by cy dy 0 s a solution y 2te2 6e t sin 3t for real numbers a b c and d hen
Algebra
Matrices & DeterminantsA ship is sailing due north At a certain point the bearing of a lighthouse 8 3 km away is N35 5 E Later on the captain notices that the bearing of the lighthouse has become 344 E How far did the ship travel between the two observations of the lighthouse The ship travelled km between the two observations Do not round until the final anewer Then round to the nearest tenth as needed
Algebra
Matrices & Determinants1 2 3 1 0 1 X 3 2 y 2 Y 2 3 y 2 a Y 24 19 y 2 y 21 y 2 y 2 200 exponen y they show exponential growth or decay x y 9 8 7 10 S 6 5 4 3 2 3 21 Or 11 2 31 1 2 3 4 5 6 7 8 9 6
Algebra
Matrices & DeterminantsWhich angles are supplementary to each other 25 and 24 2 1 35 4 22 and 21 24 and 23 21 and 24
Algebra
Matrices & Determinants3 Below is a Venn diagram illustrating the primary language spoken in the home at one of our local high schools all answers are to be to the nearest 10th of a percent Spanish 33 3 8 35 Chinese 13 English a 3pts How many students participated in the survey b 3pts Choosing a home at random what is the probability they speak only in the household English c 3pts Choosing a home at random what is the probability they speak Spanish in the household d 3pts Choosing a home at random what is the probability the speak English and Chinese e 3pts Choosing a home at random what is the probability th speak Chinese and English and Spanish in the household
Algebra
Matrices & DeterminantsDetermine if the columns of the matrixx form a linearly independent set 13 3 0 3 10 7 2 29 2 8 Select the correct choice below and if necessary Mil in the answer box es within your choice OA The columns of the matrix do not form a linearly independent set because there are more entries in each vector Type whole numbers man there are vectors in the set OB The columns of the matrix do not form a linearly independent set because the set contains more vectors than there are entries in each vector Type whole numbers OC Let A be the given matrox Then the columns of the matrix form a linearly independent set since the vector equation Ax 0 has only the trivial solution OD The columns of the matrix form a linearly independent set because at least one vector in the set is a constant multiple of another
Algebra
Matrices & DeterminantsGraph the image of AVWX after the following sequence of transformations Translation 8 units right and 16 units up Rotation 90 counterclockwise around the origin 14 12 10 8 6 4 2 14 1 2 10 8 6 4 2 X 2 V 4 6 8 1 0 1 2 1 4 N 2 4 6 W ES 8 10
Algebra
Matrices & DeterminantsWhich two triangles are congruent by the SAS Theorem Complete the congruence statement F J HHH E H H D I S 1 R HHH
Algebra
Matrices & Determinantsa Use the cross multiplication method to calculate the determinant of matrix A b Use the cross multiplication method to calculate the determinant of matrix B c Use the co factor expansion method to calculate the determinant of matrix C 2 3 2 31 3 2 2 20 3 3 0 2 One mark will be taken off for not choosing the best row or column to perform your calculation for part c Note
Algebra
Matrices & Determinants1 1 We put V v1 2 and W 3 Let t and w a Compute an R basis of Vnw b Compute an R basis of V W W be vectors in R
Algebra
Matrices & Determinantsnd the rank and nulity of the matrix A 0 1 1 2 1 1 1 0 2 with entries in ZZ3 Rank number of leading ones in its RREF Nulity number of columns without leading ones in its RREF
Algebra
Matrices & DeterminantsConsider the following piecewise defined function 2 x 5 5 if x 5 36 5 if x 5 X 9 Step 1 of 3 Evaluate this function at x 10 Write the exact answer Do not round If the answer is undefined write Und as your answer Answer 2 Points f x f 10 Keypa Keyboard Shorte
Algebra
Matrices & Determinants2w 2w w 6 54 4 v 2x 2 y 42 486 32 5y z 2y 4z AnswerHow to enter your answer opens in new window 2 Points Selecting a checkbox will replace the entered answer value s with the checkbox value If the checkbox is not selected the entered an 11 y Z Not Possible
Algebra
Matrices & Determinants3 Solve the following system of linear equations using the inverse of the coefficient matrix Use the inversion algorithm to find the inverse x 8z 1 2x 4y 6z 1 2x 5y 3z 2 035
Algebra
Matrices & Determinants4 Find the determinant of the following matrix using elementary row operations 4 2 2 B 2 2 6 3
Algebra
Matrices & Determinants11 Find the volume of the parallelepiped made by u 3 2 6 v 1 2 7 and w 2 0 2
Algebra
Matrices & Determinants6 Let u 3 2 6 and a 1 2 7 find the vector component of u along a and the vector component of u orthogonal to a
Algebra
Matrices & Determinants10 Find the area of the triangle determined by points A 2 2 0 B 0 4 3 and C 1 0 2
Algebra
Matrices & Determinants10 range of this exponential function 8 6 4 yly 3 all real numbers yly 3 yly 3 yly 3 2 104 8 6 4 2 0 2 4 6 8 10 2 4 6 8 X 10 A
Algebra
Matrices & DeterminantsLet A 0 0 0 where r is a real number Answer the following questions 0 1 Find all eigenvalues of A and the corresponding eigenvectors 2 Find an expression for A for any positive integer n 3 Find an expression for Q LA12 Please help me with a solution to Question 3
Algebra
Matrices & DeterminantsDetermine whether the set of vectors in M22 is linearly independent or linearly depender 2 3 S C JE 14 9 DE S
Algebra
Matrices & DeterminantsDawson wants to pay a 500 credit note that is due in 1 year His creditor is will ing to accept early payment of the loan by discounting it at 3 5 annual interest com pounded monthly How much can Dawson pay today to eliminate his debt
Algebra
Matrices & DeterminantsWe find the domain by finding all real inputs Step 2 The domain includes all real numbers except inputs x values that result in real outputs 1 values that result in a denominator of Select and 2 values that result in an even root of Select C outputs y values For the function y x 8 there are no such restrictions on the domain When there are no restrictions the domain of a function consists of all real numbers because there are no exclusions The inputs come from all values on the real number line which span from negative infinity to positive infinity Enter the domain of the function y x 8 using interval notation
Algebra
Matrices & DeterminantsGiven is a equilateral triangle What colours do you need to specify for the vertices in order to make the centre point light grey RGB value 2 3 2 3 2 3 Select one O a The vertices must be cyan red and yellow O b The vertices must be red green and blue O c O d The vertices must be red yellow and blue O e The vertices must be cyan magenta and yellow The vertices must be magenta green and blue
Algebra
Matrices & DeterminantsConsider the point P represented in 3D homogenous coordinates as P What statement about p the transformed point P after first performing a translation by O a O d P O b None of the others O c O e P P 2 P COON CON 3231 Toor TTO then a rotation by 90 degrees around the z axis then a scaling by 2 in the x and y axes is tru
Algebra
Matrices & Determinants5 Let G Z9 X Z12 X Z16 a Find all subgroups of G of order 144 b Let H 3 3 6 the cyclic subgroup of G generated by 3 3 6 Determine G c Determine the order of the element 4 5 2 H in the factor group G H
Algebra
Matrices & DeterminantsGiven the diagram below U 1 5 A B V 9 2 answer the following questions W Which of the vectors A B or C also represents the vector u Choose B Which of the vectors A B or C also represents the vector v C Which of the vectors A B or C represents the resultant vector u v A none of thes
Algebra
Matrices & DeterminantsLet G be the solid in the first octant that is inside cylinder x y 4 outside the 2 sphere x y z 2 4 and between the planes y 0 and y x 3 1 Find the volume of G using a triple integral in spherical coordinates 2 Set up do not evaluate an iterated triple integral in cylindrical coordinates equal to mass of G if the density at any point x y z 2 in G is 6 x y z x 1
Algebra
Matrices & DeterminantsA chemical manufacturer wants to lease a fleet of 28 railroad tank cars with a combined carrying capacity of 420 000 gallons Tank cars with three different carrying capacities are available 6 000 gallons 12 000 gallons and 24 000 gallons How many of each type of tank car should be leased Let x be the number of cars with a 6 000 gallon capacity x be the number of cars with a 12 000 gallon capacity and x3 be the number of cars with a 24 000 gallon capacity Select the correct choice below and fill in the answer boxes within your choice OA The unique solution is x and x3 Simplify your answers B There are multiple possible combinations of how the tank cars should be leased The combinations are obtained from the equations X 2t 49 x 3t 77 and x3 t forsts Simplify your answers Type integers or simplified fractions OC There is no solution X
Algebra
Matrices & DeterminantsIn Exercises 33 36 write each matrix equation as a system of linear equations without matrices 33 2 3 30 1 34 13 90 9 3 kontroll 2 0 1 0 1 1 0 35 03 1 0 1 36 0 1 0 0 1 1 37 x 5 10 0 y 6 In Exercises 37 42 AX B a Write each linear system as a matrix equation in the form b Solve the system using the inverse that is given for the coefficient matrix The inverse of 266 2 7 277 2x 6y 6z 8 2x 7y 6z 10 2x 7y 7z 9 6 is
Algebra
Matrices & DeterminantsExercise 7 2 6 Find A4 for the matrix 1 0 0 1 1 02 002 A 0 000 1 0 of Exercise 7 1 8 using the eigenvalues and eigenvectors of A
Algebra
Matrices & DeterminantsGive an example of matrices A B M2x2 such that null A B is not a subset of either null A or null B
Algebra
Matrices & DeterminantsWhich one of the following is a subspace of M2x2 20 a b a d a b 8 1 a b a b a b 0 c d 1 d
Algebra
Matrices & DeterminantsFind all matrices A of the form 0 A 5 0 0 6 5 1 6 0 1 0 0 0 0 0 N 0 X Y 0 Z 0 0 0 0 such that AB Your last answer was interpreted as follows 0 00 000 22 BA where B is the matrix This answer is invalid Your answer contains question mark characters which are not permitted in answers You should replace these with a specific value The variables found in your answer were 2