Matrices & Determinants Questions and Answers

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

Suppose you make a 4-minute local call using a calling card and are charged 7.6 cents. The cost of a local call varies directly with the length of the call. How much more will it cost to make a 30-minute local call? Select one: O a. More than $0.50. Ob. $0.50 O c. Not enough information is given. O d. Less than $0.50

A personal account earmarked as a retirement supplement contains $342,400. Suppose $300,000 is used to establish an annuity that earns 4%, compounded quarterly, and pays $6500 at the end of each quarter. How long will it be until the account balance is $0? (Round your answer UP to the nearest quarter.) __ quarters

Exer. 7-8: Identify any vertical asymptotes, horizo asymptotes, and holes. -2(x + 5)(x-6) (x - 3)(x - 6) (7 f(x) = =

SOLVE, GRAPH AND WRITE IN INTERVAL NOTATION -3 ≤2x+1≤7 -10<2(3x+5) <16 13> 3x+4>-2 -2<-x-5<1

Use matrices to solve the system of linear equatio W of the parameter a.) (2x (x, y, z) www www www 2y - Sy 3z 318,408,144 X

(optional) Solve by the substitution method: 2xy +32 = 8 x+y+z=9 3x - 5y + 2z = -7 (i)

Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the following matrix: 6 4 -9 A 0-3 0 1 0 -4 The characteristic equation is NOTE: Enter the eigenvalues in increasing order. Eigenvalues A = Bases for the eigenspaces Choose one Choose one = 0

Solve the system of equations by any method. -4x+8y = 36 x-2y=-9 Enter the exact answer as an ordered pair, (x, y). If there is no solution, enter NS. If there is an infinite number of solutions, enter the general solution as an ordered pair in terms of x. Include a multiplication sign between symbols. For example, a * x.

The following is a conic section with a focus at the origin. Please classify the conic section and provide the polar and rectangular equations. 1) eccentricity: 0.5, vertices: (0, 4/7), (0, -4) 0.7, vertices: (14/19, 0), 2) eccentricity: (-14/5, 0)

solve the linear system X, X, +5X, - X =0 x₁ + x₂ -2x, +3x₁ = 0 3x, x₂ +8x₂ + x₁ = 0 x, +3x₂ -9x, +7x₁ = 0

Given the linear system: -x+y+2z = a 2x-1y+Bz = 3 1x-ly+2z=3 Find the values of a and ß, if any, such that the system: a) has one single solution, and give the solution. b) has infinite solutions, and give the solutions. c) has no solutions.

Show that U = {(x, y, z)| -x + 2y + 3z = 0} is a subspace of R³.

Use the backward substitution method to solve the system of equations. If the system is inconsistent, explain. If the system is consistent but has infinite solutions, write correct parametric equations. Make sure you label each step by showing the corresponding correct row operations in symbolic form as shown in class. 20x-10y- 5z = 25 -8x+4y+2z=10 -x+3y+4z=-3

Let L : R² → R³ be the function defined by L. ([*2)) = 1) Show that L is a linear transformation 2) Find ker(L) 3) Find range (L) 4) If S = span{e₁,e₂} find L(S)

Let f₁ = (2,0,1), f₂ = (-1,1,3), and f = (0, -2, 1). (a) Show that the set F= {f₁.f₂. fs} is linearly independent. Thus, show that F is a basis for R³. (b) Is the basis F positively oriented or negatively oriented? Justify your answer!

Find a 2x2 matrix A such that Av₁ = w₁, Av₁ = W₂, where v₁ = (2,5), w₁ = (3,2). v₂ =(3,2), W₂ = (5,2).

If one of the eigenvalues of an n x n matrix A is 0, then which of the following statements must be true? A is not diagonalisable. The determinant of A is 0. The column space of A is n-dimensional. The solution to Ax=b is unique for all bR".

The goal of this problem is to fit a quadratic function of the form f(x) = c₁x² + ₂x to the data points (-3,-82), (0, -1), (1, -2), (3, -82), using least squares. (a) The problem is equivalent to finding the least squares solution to the system Xc = y where X = C2 || 3 (b) Find the coefficients of the best fit by finding the least squares solution to the system in part (a) C1 || y = and c = [C₁, C₂]

Complete the analytic proof for the following. 2. The line segments that join the midpoints of the opposite sides of a quadrilateral bisect each other.

Case Study - Math in Animal Science 5. Cattle feeds are specifically formulated to meet the nutritional needs of the cattle. A rancher wants to formulate 2,400 pounds of feed containing 14% crude protein using corn (8.8% crude protein) and a protein supplement (38% crude protein). How many pounds of each should the rancher use to make the feed mix? Setup a system of equations and solve. Round your answers to one decimal place and label them.

describe each dilation and reflection as it relates to the parent function y=-6x

f First find f+g, f-g, fg and Then determine the domain for each function. g f(x) = 4x² - 15x -54, g(x)=x-6 (f+g)(x) = (Simplify your answer.)

Fifteen years after investing $20,000, a retired couple notices that their investment is worth $28,250 (including simple interest). Find the annual interest rate their money earned during that time. Round to the nearest tenth of a percent.

Solve the following system of linear equations. x1 + x2 + 2x3 = 1 x1 + 2x2 - x3 = -2 x1+ 3x2 + x3 = 5.

Use Solver to solve this problem Consider the linear programming problem. Maximize : 6x + 5y + 4z Subject to: 2x +y +z ≤180 x+3y+2z ≤ 300 2x+y+2z ≤ 240 x ≥ 0, y 20, z 20

Let u =(3, 2,-1), v = (0, 2,-3), and w=(2, 6, 7). Compute the indicated vectors. (a) u x (v Xw) (b) (u X v) X w

Find a unit vector orthogonal to both u and v. u = -3i+2j+ 5k v = 1/2i - 3/4j +1/10k

Given A={{11,3,4},{-9,1,-5},{-12,-2,-5}} Observe that the first column plus twice the second column equal the third column. Find a nontrivial solution Ax=0

For questions 8 through 10, consider the function f(x) = 4x³-7x-3. Lasitsmit pidus ort robizu voiled 20 slo dergelus? 8. Use the Rational Zeroes Theorem to list all the possible rational zeroes. 02 9. a. Use synthetic division to evaluate f(5). Show your work below. b. 1. Is 5 an upper bound on the real zeroes of f(x)? 2. How do you know? c. 1. Is 5 a lower bound on the real zeroes of f(x)? 2. How do you know? mol bono

Find the volume of the parallelepiped with sides u, v, and w. u = (2,−6, 2), v = (0, 4,−2), w = (2, 2,-4)

Solve the system of linear equations by graphing. y = - 4x 2x+y = -2 Use the graphing tool to graph the system. Click to enlarge graph C Points: 0 of 1 Q Q

Find the area of the triangle bounded by the lines: x - 2y - 2 = 0, 7x - 4y - 34 = 0, 3x-y- 11 = 0.

Which of the following statement(s) is (are) true? ● 1. B) A) I and II C) 1 The set of all 2x2 matrices of the form [] with the standard operations is a vector space The set of all 2x2 matrices of the form with the standard operations is a vector II and III D) III space The set of all 2x2 matrices of the form with space E) II with the standard operations is a vector

Which of the following set is a basis in R* (1) S₁ = {(1,1,1,1), (0,0,0,0)} S₂ = {(1,0,1,0), (1,2,3,4), (1,0,0,1)) S3 = {(1,-1,1, -1), (1,0,0,0), (1,0,1,0), (0,0,0,1)) S4= {(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,4,0)) (IV) OA) (II) B) None O) (M) OD) (1) E) (III)

Consider points A(1,4,7), B(2, -1,3), C(3, 5, 3), A'(2,3,5), B'(1, 1, −1) and C'(1, -4,-2). Find a point P and a line h such that triangles ABC and A'B'C' are in perspective from a point P and from the line h, in which A corresponds to A', B corresponds to B' and C corresponds to C'.

On the graph of f(x) = sinr and the domain 0 < x < 2, for which of the following intervals is f(z) strictly decreasing? Choose all correct answers. Select all that apply: □ (0,5) (1) □ (1,4) (3, 2)

(1 point) Find the matrix A of the linear transformation T from R2 to R² that rotates any vector through an angle of 135° in the counterclockwise direction. E

The number of hours of daylight in Boston is given by [365 (x-79)] + 12, h(x) = 3 sin where x is the number of days after January 1. (1 point for each part) (You can use a calculator) a) What is the period of this function? b) How many days after January 1 is the longest day of the year? c) How many hours of daylight are there on the longest day of the year? d) How many days after January 1 is the shortest day of the year? e) How many hours of daylight are there on the shortest day of the year?

5. You are given three vectors below. It is known that these vectors are on the same plane. Determine the value of t=? (15 pts) 183 A) t = -4 B) t=0 C) t =4 D) any value of t satisfies E) More than one answers are correct F) None of them.

Is q= 0.5 0.6 a steady-state vector for A= 0.4 0.5 0.6 0.5 ? Justify your answer. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The vector q is a steady state vector because the sum of its entries is 1 and Aq=q. OB. The vector q is not a steady state vector because Aq= (Type an integer or decimal for each matrix element.) OC. The vector q is not a steady state vector because the sum of its entries is (Type an integer or a decimal.)

In class, we discussed how a point and a nonzero vector emanating from it completely determine a line. Explain how this affine representation (point plus vector) is equivalent to those of symmetric equations in space: (x-a)/b = (y- c)/d = (ze)/f. Provide a concrete example to illustrate your explanation.

22. Suppose that A € M4x4(R) and b € R¹ are A= 1 2 1 -1 123 5 365 2 122 2 (a) (2.5%) What is N(A)? (b) (2.5%) What is the solution x of Ax = b? and b=

The point (2, -1) is on a function. State the corresponding point on the inverse relation. a) (-1, -2) Ob) Can't find it without the original function. Oc) (-1,2) d) (1, -2)

Simplify. Write the answer using positive exponents. X What is raising a quotient to a power? OA. For any numbers a and any integers m and n, (am)" = amn B. For any numbers a and any integers m and n, am an -5 C. For any numbers a and b, and any integer n, Use (8)" = OD. For any numbers a and b, and any integer n, (ab)" = a^b^. bn X an b b" -4)-5 to start simplifying the expression. = X -4- =am-n 4.0 (3)^= an b#0.

Find the intersection of the following planes by letting z = t. 5x - 4y + z-1 = 0 X-Z+3=0

Let u= (-2, 6, 1). Find ||u||. Use that to find a unit vector that points in the direction of u. Write your answers in exact form, using sqrt() to indicate square roots. Enter the vector using <and > as enclosing brackets. ||u|| Unit vector that points in the direction of u

Solve the system of equations using Gauss-Jordan elimination. x+2y-z = 0 2x + z = -1 x - y = 1 a. Write the system of linear equations as a matrix equation Ax = b. b. Determine A-¹ using the Gauss-Jordan method. c. Solve for x using A-1 and b from above.

Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. -9x1² - 6x₁x2-x₂² What is the most precise classification for the quadratic form? A. Indefinite B. Positive semidefinite C. Negative definite D. Positive definite E. Negative semidefinite

Evaluate 2x -y for the given replacement values. x = 2 and y = -9 2x-y=