Matrices & Determinants Questions and Answers

1 Write the inverse of the function f x 3x 9 using the f x notation

5 Find a series bm fe bn 0 n 0 x 2 dx

f Aspect Ratio 16 9 Exceeded 00 If both the 4 3 and the 16 9 screen had a height of 25 inches find the follow measurements ct ratios hat percent of the screen is filled with the 4 3 picture 752736670 View Neftali Moreno Miranda Attempt 1 f Aspect Ratio 4 3 x

B 10 2 4 4 1 2 12 3 7 B 7 2 16 3 1 8 6 2 20 x Br a Find the transition matrix from B to B p 1 2 3 P pp 1 16 40 19 3 7 5 12 b Find the transition matrix from B to B 1 0 7 0 18 1 5 6 3 5 10 c Verify that the two transition matrices are inverses of each other 0 1 21 7 0 53 5 4 25 32 16 0 0 1 d Find the coordinate matrix x g given the coordinate matrix x g

Let T be an operator on a finite dimensional complex vector space V Which of the following is NOT always true Select one O a V has a basis consisting of eigenvectors of T O b Oc V is the direct sum of the generalised eigenspaces of T If A is an eigenvalue of T then T AI G is nilpoent O d If U Um are generalised eigenvectors of T corresponding to distinct eigenvalues then V Um are linearly independent

actorization of this matrix 11 3 1 1 1 1 C 5 4 4 3 2 1 4 2 7 1

Find the quotient using long division 3x 9x 3 X 5 3x 9x 3 X 5 Simplify your answer C

6 Find a least square solution of 1 1 2 2x 1 1 1 0 1

mutritionist is studying the effects of the nutrients folic acid choline and inositol He has three types of food available and each type contains the following amounts of these trients per ounce 1 1 0 a Find the inverse of the matrix below and use it to solve the remaining parts of this problem 34 1 Folic acid mg Choline mg Inositol mg Type A Type B Type C H 1 1 1 3 Type B Type C 1 1 3 2 1 1 2 11 2 4 1 2 OZ Oz oz Type A 3 1 1 b How many ounces of each food should the nutritionist feed his laboratory rats if he wants their daily diet to contain 20 mg of folic acid 14 mg of choline and 8 mg of inositol OZ Type B 4 1 1 11 OZ Type C 1 3 1 c How much of each food is needed to supply 11 mg of folic acid 11 mg of choline and 5 mg of inositol Type A OZ d Will any combination of these foods supply 2 mg of folic acid 3 mg of choline and 1 mg of inositol quired supply

A survey of 850 people reported that between 38 6 and 45 4 favored the reelection of the current governor Find the margin of error

heh s group takes a survey to determine the education and income of its members Matrix A summarizes the proportions of members in various categories of years of ostsecondary education and income Matrix B shows the total number of members in each income category None 1 to 4 More than 4 Less than 50 000 0 75 0 25 0 Less than 50 000 50 000 to 100 000 Income level 50 000 to 100 000 0 20 0 40 100 000 or more 10 Total 4 20 a Calculate the product matrix AB 0 40 B 100 000 or more 0 0 20 0 80 A b Interpret the entries of the matrix AB Each entry gives the percentage of group members with the related amount of postsecondary education O Each entry gives the total percentage of group members in the relevant income bracket OEach entry gives the total income at the relevant education level O Each entry gives the number of group members with the related amount of postsecondary education alrot

Carry out the indicated algebraic operation If not possible enter IMPOSSIBLE in any cell of the matrix 3 A 3 2 5 D 39 G 3 5 a ABE B 7 10 1 5 8 0 3 4 4 b AHE E H 3 1 1 2 0 5 2 1 2 3 C F 3 0 3 2 100 0 1 0 0 0 1

olve the matrix equation for the unknown matrix X If not possible enter IMPOSSIBLE in any cell of the matrix 91 16 23 37 50 07 X D C X A C B D 65 4 3 30 20 20 20 10 0 11

Consider the following u 2 4 v 1 1 a Calculate proj u proj u b Resolve u into u and u where u is parallel to v and u is orthogonal U

3 Find a least squares solution of the system Ax bifA 2 46 46 1 2 and b 8

Find the equation for the parabola that has its vertex at the origin and has directrix at x = -1/48

Solve the following system of equations using Elimination, 5x + 4y = -30 3x - 9y=-18

Consider the following quadratic function. Step 2 of 4: Find the line of symmetry of this function. y = -(x + 4)² +3

Write a polar equation of a cardioid that passes through (4,0), (4, π), (0,0). Find a fourth "key" point on its graph with r> 0 and 0 € [0,2m).

Which of the following statements is (are) true if all vectors are in R"? Oc) A matrix with orthogonal with orthogonal columns is an orthogonal matrix d) If W is a subspace of " spanned by n nonzero orthogonal vectors, then W = R" Statements a and b Statements b, c and d Statements a, b and d Statements a and c b)An orthogonal matrix is invertible a) Not every linearly independent set in R" is an orthogonal set Statements a, b and c

To find the diameter of a circle the radius by two 2. The number of square units that covers the inside of a circle is the 3. To find the area of a circle, you need to know the measure of its 4. A circle's radius is the distance form the edge to the 5. To find the radius, 6. To find the area of a circle use the formula 7. A common value for is 3.14 8. To find the circumference of a circle use the formula the diameter of the circle by two

Consider the following three vectors of R4: a₁ = [2, -3, 5, 1], a2 = [0,-2,-4, 2], There exists a linear equation in the coordinates [x, y, z, u] whose solution set coincides with span{a₁, a2, a3}. Determine such an equation

On a science test, a score of 91 falls exactly 1.5 standard deviations above the mean. If the standard deviation for the test is 8, what is the mean score?

The volume of a parallelepiped is six times the volume of the tetrahedron defined by the same set of vectors. What is the volume of the tetrahedron with vertices A(-1,2,3), B(3,-2, 1). C(2, 1, 3) and D(-1, -2, 4)? 54 7/2 16/3 11

The grades on a math quiz are normally distributed with a mean of 85 and a standard deviation of 4. What percent of the students scored between 81 and 89?

Find the perimeter of a square with an area of 702.25 square yards. A. 26.5 yards B. 106 yards C. 175.56 yards D. 53 yards

Find a basis for the eigenspace corresponding to each listed eigenvalue of A below. A basis for the eigenspace corresponding to A-5 is A basis for the eigenspace corresponding to A-4 is

Find the time it takes for $8,900 to double when invested at an annual interest rate of 5.3%, compounded continuously. Give your answer to 2 decimal places. Find the time it takes for $195,800 to double when invested at an annual interest rate of 5.3%, compounded continuously. Give your answer to 2 decimal places.

For the system below a. Find the equilibrium points. b. For the equilibrium point (0,50) find the associated linear system, solve it, and perform the qualitative analysis,

Is u in the plane in R3 spanned by the columns of A? Why or why not? Select the correct choice below and fill in the answer box to complete your choice. A. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. B. No, the reduced echelon form of the augmented matrix is which is an inconsistent system.

Factor A into a product QR, where Q has orthonormal set of column vectors and R is an upper triangular matrix with positive diagonal entries. (b) Solve the least squares solution x to Ax = b.

Bonnie is playing with Addison and Cooper at the park. We decide to play a game of tag, so Addison and Cooper run off in separate directions from the same starting point (Bonnie). The angle between Addison and Cooper as they run off is 100°. If Addison runs 40 feet from Bonnie, and Cooper runs 65 feet from Bonnie, how far are Addison and Cooper from each other?

Determine the value of b that would guarantee that the below linear system is consistent. x₁ - 2x₂ - 6x3 = 5 2x₁4x25x3 = -8 -2x₁ +4x29x3 =

Determine whether the set S spans R³. If the set does not span R3, then give a geometric description of the subspace that it does span. S = {(1, -6, 0), (0, 0, 1), (-1, 6, 0)) S spans R³. S does not span R³. S spans a plane in R³. S does not span R³. S spans a line in R³. S does not span R³. S spans a point in R³.

Suppose S = {r, u, d) is a set of linearly independent vectors. If x = 4r + u + 4d, determine whether T = {r, u, x} is a linearly independent set. î 1. Is T linearly independent or dependent? Select an Answer If I is dependent, enter a non-trivial linear relation below. Otherwise, enter O's for the coefficients. r+ u+ x = U.

Find the minimum and maximum values of z=9x + 2y, if possible, for the following set of constraints 4x + 3y 2 12 x + 3y 26 x20, y20

Perform the row operation(s) on the given augmented matrix. R3 = 4r1 + 13 [-7 -5 -1 1-10] 6 -2 9 5 28 -6 6 18 O-7 -5 -1-10 6-29 5 0 16 10-22 -7 -5 -11-10] 6 -2 9 5 0-26 2-22 10 O [-7 -5 -1/-10] 6-29 5

Suppose S {r, u, d) is a set of linearly independent vectors. If x = 4r +u+ 4d, determine whether T = {r, u, x} is a linearly independent set. Select an Answer 1. Is T linearly independent or dependent? = If I is dependent, enter a non-trivial linear relation below. Otherwise, enter O's for the coefficients. r+ u+ x = U.

a) [15 pts] Determine whether the matrix M = [14] belongs to span{A₁, A₂, A3} if 04 0-3 A₁-[88] 4₂-[8] and A-[-44] = = 100 b) [5 pts] What is the dimension of the vector space M5 5?

Using the standard Euclidean inner product in R2 find an orthogonal basis for W = span({(1, -1, 0, 1), (1, 0, 1, 1), (1, 2, 1, 3)}) List the vectors of this orthogonal basis by entering 1 vector into each box. If you have entered all your basis vectors, type "X" into any remaining answer boxes.

el ul A patient takes vitamin pills. Each day he must have at least 360 IU of vitamin A, 4 mg of vitamin B₁, and 90 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 1 mg of vitamin B₁, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B₁, and 35 mg of vitamin C. Pill 1 costs 10¢, and pill 2 costs 30¢. Complete parts a and b below. ... a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? of pill 2. The minimum cost is $. He should buy of pill 1 and (Simplify your answers. Type integers or decimals.) b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. mg of vitamin C more than he needs. He is receiving IU of vitamin A, mg of vitamin B₁, and (Simplify your answers.)

Find the minimum and maximum values of z = 9x + 2y, if possible, for the following set of constraints 4x + 3y 2 12 x+3y26 x20, y 20 QUEDAB Select the correct choice below and, if necessary, fill in the answer box to complete your choice (Round to the nearest tenth as needed.) A. The minimum value is OB. There is no minimum value.

(16 points) Let T: P3 → P3 be the linear such that transformation T(2x²) = 4x² + 4x, T(-0.5x - 5) = 2x² + 3x + 2₂ Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers.

Let A and B be 3 x 3 matrices such that matrix A is symmetric matrix. If given that 1 det (A) and det (B) = -2 then evaluate: 2 det (B³ adj(24¹)).

(a) Multiply the binomials (4x-5y)². (b) How do you factor 16x²-40xy+25y²?

2. 7: R5 → R¹ is a linear transformation with the standard matrix A = (a) Find a basis and the dimension for Row(A). (b) Find a basis and the dimension for kernel(T). (c) Find a basis and the dimension for range(T). (d) Find the rank of A. 11 -1 10-2 102 1 0 1 14 1 -1 0 02 -1 -

The cost to produce x units of wire is C=60x+600, while the revenue is R 85x Find all intervals where the product will at least break even. Select the correct choice below and, if necessary, fill in the answer box to complete your choice OA. The inequality in interval notation is OB. The product will never break even

The function f(x) = x + 18 is one-to-one. Find an equation for f1(x), the inverse function. f-¹(x) = [ (Type an expression for the inverse. Use integers or fractions for any numbers in the expression.)

Determine the x- and y-intercepts of the following equation. Then graph the equation. 6x - 5y = -30 x-intercept: y-intercept:

Use the following functions to solve each question below. Simplify completely. f(x) = x² + 8x - 17 g(x) = 2x + 3 a. (4)(x) = b. (f+g)(x) = c. (f - g)(x) = I