Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

Tutors Answer Your Questions about Linear Algebra (FREE)

Question 1202265: Would like information on the method of solving (and what branch of mathematics) is involved in:
f(x+h)g(x) * f(x)g(x+h). f(x) divides f(x+h)g(x) which means there exists some polynomial k(x) such that f(x+h)g(x) =f(x)k(x).
I thought it had to do with polynomial math but apparently not.
Click here to see answer by mananth(16946)

Question 1202277: One safe investment pays 6% per year, and a more risky investment pays 12% per year. a. How much must be invested in each account if an investor of $102,000 would like a return of $7,800 per year? b. Why might the investor use two accounts rather than put all the money in the 12% investment?
Click here to see answer by math_tutor2020(3816)

Question 1202528: using graph find the maximum & minimum value of the objective function subject to the given constraints .
objective function: s= 2x + 7y
subject to :{5x +y >=5
x + 3y >=9
x>=0
y>=0
Click here to see answer by Theo(13342)

Question 1202713: What is the algebraic expression for the mathematical statement "Seven more than thirteen times a certain number p".
Click here to see answer by Theo(13342)

Question 1202712: What is the equation for Seven more than thirteen times a certain number q.
Click here to see answer by josgarithmetic(39616)

Question 1202726: Find an equation of the line that passes through (2, -2) and parallel to the line passing through (4, 5) and (6, 4).
Click here to see answer by josgarithmetic(39616)

Question 1202730: Questions 1) The midpoint of AB is at (0,3). If A=(0,−2), find B.

Questions 2) Write the equation of the circle centered at
(0,−6) that passes through (−5,−18).

Click here to see answer by Alan3354(69443)

Question 1202894: The following is an example of a linear programming problem.
Maximize:
P=3x−7y
subject to:
x^2−4y≤0
3x−y≤18
x≥0
y≥0
True Or False
Click here to see answer by math_tutor2020(3816)

Question 1202913: Solve the following linear programming problem.
Maximize
P = x + 4y − 2z
subject to
3x + y − z ≤ 80
2x + y − z ≤ 40
−x + y + z ≤ 80
x≥ 0, y≥ 0, z≥ 0

Write the objective function in standard form.
Click here to see answer by Edwin McCravy(20054)

Question 1202912: Consider the following simplex tableau.
x y u v P Constants
1 1 1 0 0 1
1 0 −1 1 0 5
5 0 7 0 1 18

Since the simplex tableau is in final form, write the optimal solution and the optimal value.
Optimal Solution:
(x,y) =

Optimal Value:
P =18

Click here to see answer by Edwin McCravy(20054)

Question 1202927: CalJuice Company has decided to introduce three fruit juices made from blending two or more concentrates. These juices will be packaged in 2-qt (64-oz) cartons. One carton of pineapple-orange juice requires 8 oz each of pineapple and orange juice concentrates. One carton of orange-banana juice requires 12 oz of orange juice concentrate and 4 oz of banana pulp concentrate. Finally, one carton of pineapple-orange-banana juice requires 4 oz of pineapple juice concentrate, 8 oz of orange juice concentrate, and 4 oz of banana pulp concentrate. The company has decided to allot 16,000 oz of pineapple juice concentrate, 24,000 oz of orange juice concentrate, and 5000 oz of banana pulp concentrate for the initial production run. The company also stipulated that the production of pineapple-orange-banana juice should not exceed 800 cartons. Its profit on one carton of pineapple-orange juice is $1.00, its profit on one carton of orange-banana juice is $0.80, and its profit on one carton of pineapple-orange-banana juice is $0.90. To realize a maximum profit, how many cartons of each blend should the company produce?
pineapple-orange juice ____ cartons
orange-banana juice ___ cartons
pineapple-orange-banana juice 800 cartons
What is the largest profit it can realize?
$ ______

Are there any concentrates left over? (If so, enter the amount remaining. If not, enter 0.)
pineapple concentrate
0 oz
orange concentrate
0 oz
banana pulp concentrate
____ oz

Click here to see answer by Theo(13342)

Question 1202954: A canning company produces two sizes of cans—regular and large. The cans are produced in 10,000-can lots. The cans are processed through a stamping operation and a coating operation. The company has 30 days available for both stamping and coating. A lot of regular-size cans requires 2 days to stamp and 4 days to coat, whereas a lot of large cans requires 4 days to stamp and 2 days to coat. A lot of regular-size cans earns $800 profit, and a lot of large-size cans earns $900 profit. To fulfill its obligations under a shipping contract, the company must produce at least nine lots. The company wants to determine the number of lots to produce of each size can ( and ) to maximize profit. How to solve the problem using simplex method?

Click here to see answer by ikleyn(52775)

Question 1202966: Consider the following final tableau corresponding to a linear programming problem.
x y z u v w P Constants
0 0 −1/2 1 −1/4 −1/4 0 2
0 1 0 0 1/4 −1/4 0 3
1 0 3/2 0 0 1/2 0 15
0 0 1 0 3/2 1/2 1 78
Part 1 of 2
(a.) How many solutions does the linear programming problem have?
One Solution
Part 2 of 2
(b.) Since the linear programming problem has one solution, provide the solution as a point.
(x, y, z) = ( , , )

Click here to see answer by Edwin McCravy(20054)

Question 1202965: Consider the following final tableau corresponding to a linear programming problem.
x y u v w P Constants
0 0 1 −23/5 12/5 0 48
0 1 0 3/5 −2/5 0 6
1 0 0 −2/5 3/5 0 21
0 0 0 0 5 1 375
Part 1 of 2
(a.) How many solutions does the linear programming problem have?
Infinite Solutions
Part 2 of 2
(b.) Since the linear programming problem has infinitely many solutions, describe the line segment containing the solutions by providing two points. (Enter the point with the smaller x-value first.)
There are infinitely many solutions on the line segment connected by the points
(21, 6) "this is correct"
and
( , ) "I need help on the last point"

Click here to see answer by Edwin McCravy(20054)

Question 1202911: Consider the following simplex tableau.
x y z u v w P Constants
0 1/2 0 1 −1/2 0 0 9
1 1/2 1 0 1/2 0 0 0
2 1/2 0 0 −3/2 1 0 8
−1 3 0 0 1 0 1 38

Since the simplex tableau is not in final form, write the basic solution. (Also, specify whether each variable is active or inactive.)

Active Variables
(Select all that apply.)

x y z u v w P

Inactive Variables
(Select all that apply.)
x y z u v w P

Click here to see answer by Edwin McCravy(20054)

Question 1202964: Use the technique developed in this section to solve the minimization problem.
Minimize
C = x − 6y + z
subject to
x − 2y + 3z ≤ 10
2x + y − 2z ≤ 15
2x + y + 3z ≤ 20
x ≥ 0, y ≥ 0, z ≥ 0
The minimum is C = at (x, y, z) =
Click here to see answer by ikleyn(52775)

Question 1202983: ***13-12
On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was 76%. The standard error of estimate was 10. There were 24 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam. (Round your DF answers to nearest whole number and other answers to 2 places.)

Click here to see answer by Jason57t(3)

Question 1203447: Determine which of the following maps f are linear:
1. f : R
3 → R2
2 defined by f(x, y, z) = (x, z)
Click here to see answer by ikleyn(52775)

Question 1203509: Jolene invests i her savings and two bank accounts, one paying 5% and the other paying 12% interest per year she puts twice as much in the lower-yielding account because it’s less risky. If she earned $4202 of total interest for the year, how much was invested in each account?
She invested $ in the account earning 5% interest.
She invested $ in the account earning 12% interest.
Click here to see answer by josgarithmetic(39616)

Question 1203508: You are choosing between two different cell phone plans. The first plan charges a root of $.22 per minute. The second plan charges a monthly fee of $29.25 plus 12 cents per minute. Let t be the number of minutes you talk and C1 and C2 be the cost(in dollars) of the first and second plan. Given equation in terms of t, and then find the number of talk minutes that would produce the same cost for both plans.
C1=
C2=
Click here to see answer by josgarithmetic(39616)

Question 1203507: We have a jar of coins, all quarters and pennies. Altogether, we have 247 coins, and the total value of all coins in the jar is $41.35. How many quarters are in the jar?
Answer: quarters
Click here to see answer by josgarithmetic(39616)

Question 1203794: You are going to rent a car for a day. You have two choices, Golden Car Rental and Classic Car Rental. Golden Car Rental will rent you the car for $35 a day with unlimited mileage while Classic Car Rental will rent you the car for $15 a day plus $.80 a mile. Write an equation for the cost of renting a car from Golden Car Rental. Write an equation for the cost of renting from Classic Car Rental
Click here to see answer by math_tutor2020(3816)

Question 1203816: 2.
(a) Let 3x − 2y + 4z = 11 and 2x − 5y + 3z = 3 be two planes. Then P = (7, 1, −2)
are on both planes. Let ℓ be the line of intersection of these two planes. Find a
parametric equation for ℓ.
(b) With the same two planes as in (a), we know that Q = (21, 0, −13) is on both
planes. Find another parametric equation for ℓ. Find a relation between the two
parametrizations in (a) and (b).
Click here to see answer by ikleyn(52775)

Question 1203800: 2.
(a) Let 3x − 2y + 4z = 11 and 2x − 5y + 3z = 3 be two planes. Then P = (7, 1, −2)
are on both planes. Let ℓ be the line of intersection of these two planes. Find a
parametric equation for ℓ.
(b) With the same two planes as in (a), we know that Q = (21, 0, −13) is on both
planes. Find another parametric equation for ℓ. Find a relation between the two
parametrizations in (a) and (b).
Click here to see answer by ikleyn(52775)

Question 1203799: Write u = (3, 2, −6) as a sum of two vectors, one parallel and one orthogonal to
w = (2, −4, 1).
Click here to see answer by ikleyn(52775)

Question 1203927: Solve this system using the substitution method. -2x - y = -7 x + 7y = 10 Solve using the substitution method and be sure to show all of your work.
Click here to see answer by MathLover1(20849)

Question 1204100: Consider the system of equations
x + 2y - 3z = a
2x + 6y - 11z = b
x - 2y + 7z = c
where a, b and c are three real numbers.
1 What relation must the parameters a, b and c satisfy for the system of equations to have at least
the system of equations has at least one solution?
2. Assuming that a, b and c satisfy the relation that allows the system to have at least one solution, what relation must a, b and c satisfy?
the system has at least one solution, calculate in function of a, b and c, the general solution of the system of equations using Gauss's method.
Can the above linear system have a unique solution in R3?
Click here to see answer by MathLover1(20849)

Question 1204146: In an examination adenike obtained 19 marks more than musa. If adenike had obtained one and a half time her own marks she would have scored 6 marks more than Musa’s marks. Find the marks scored by each of them
Click here to see answer by ikleyn(52775)

Question 1204271: Use a graphing calculator to approximate the partition numbers of f(x). Then solve the inequalities A) f(x) > 0 and B) f(x) < 0
f(x) = x^4 - 4x^2 - 3x + 5
what are the partition number(s) of f(x)?

Can you please explain to me this homework question step-by-step? Thank you
Click here to see answer by ikleyn(52775)

Question 1204555: what is the slope and y intercept for y=3-4x
Click here to see answer by mananth(16946)

Question 1204775: Find the price that will maximize profit for the demand and cost functions, where p is the price, x is the number of units, and C is the cost.
Demand Function Cost Function
p = 80 − 0.1sqrtx C = 35x + 600

Click here to see answer by MathLover1(20849)

Question 1205327: An individual needs a daily supplement of at least 510 units of vitamin C and 266 of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 102 units of vitamin C and 19 units of vitamin E, while each ounce of food II contains 51 units of vitamin C and also 38 units of vitamin E. The total supplement of these two foods must be at most 21 ounces. Unfortunately, food I contains 19 units of cholesterol per ounce and food II contains 13 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. Find the minimum amount of cholesterol.
amount of food I
amount of food II
minimum cholesterol

Click here to see answer by math_tutor2020(3816)

Question 1205886: Use the pair of functions to find f(g(x))
and g(f(x))
. Simplify your answers.
f(x)=sqrt(x)+8,g(x)=x^2+3

f(g(x))=
g(f(x))=
Click here to see answer by MathLover1(20849)

Question 1205886: Use the pair of functions to find f(g(x))
and g(f(x))
. Simplify your answers.
f(x)=sqrt(x)+8,g(x)=x^2+3

f(g(x))=
g(f(x))=
Click here to see answer by Theo(13342)

Question 1206083: if z=x-8/2x, what is x
Click here to see answer by greenestamps(13198)

Question 1206490: 5x+y=-13 and -x2y=-10 solve by substitution

Click here to see answer by josgarithmetic(39616)

Question 1208221: A stadium has 50,000 seats. Seats sell for $35 in Section A, $20 in Section B, and $15 in Section C.
The number of seats in Section A equals the total number of seats in Sections B and C.
Suppose the stadium takes in $1,323,000 from each sold-out event. How many seats does each section hold?
Click here to see answer by ikleyn(52775)

Question 1205507: If TA is multiplication by a matrix A with three columns, then the kernel of TA is one of four possible geometric objects. What are they? Explain how you reached your conclusion

Click here to see answer by CPhill(1959)

Question 1206684: Hello, I need help with the following problem:
Three basis are given in the plane. With respect to those basis a point has as components (x1,x2), (y1,y2) and (z1,z2). Suppose that [y1 y2] = [x1 x2]A, [z1 z2] = [x1 x2]B and [z1 z2] = [y1 y2]C being A,B,C 2x2 matrices. Express C as a function of A and B.
I very much appreciate your help.
Click here to see answer by CPhill(1959)

Question 1200083: Let A be the matrix of coefficients of a 5 × 7 system of linear equations, A⃗x = ⃗b. Using row operations, you find that A is row equivalent to a matrix in reduced row echelon form with one row of zeroes at the bottom.
(a) What is rank(A)?
(b) How many free variables does the system have?
(c) For the given system how many possible solutions could it have? (Circle all which apply)
1. 0 solutions
2. 1 solution
3. infinite solutions
(d) For the associated homogeneous system A⃗x = ⃗0, how many possible solutions could it have? (Circle all which apply)
1. 0 solutions
2. 1 solution
3. infinite solutions
Click here to see answer by GingerAle(43)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760