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

Tutors Answer Your Questions about Linear Algebra (FREE)

Question 1168386: Find a pair of vectors u, v ∈ R2 that are orthogonal with respect to the inner product,
⟨u,v⟩=3u1v1 +2u2v2
but which are not orthogonal with respect to the Euclidean inner product,
⟨u,v⟩=u1v1 +u2v2
Click here to see answer by ikleyn(52775)

Question 1168825: Emily is creating a rectangular garden in her backyard. The length of the garden is 12 feet. The perimeter of the garden must be at least 30 feet and no more than 64 feet. Use a compound inequality to find the range of values for the width w of the garden.
Click here to see answer by josgarithmetic(39616)

Question 1168922: Sets B and B′ are both bases for P1.
B = {6+3x,10+2x}
B′ = {2,3+2x}
Find the transition matrix from B to B′.
Click here to see answer by ikleyn(52775)

Question 1169010: what is the r in the equation V = πr2h?

Click here to see answer by Alan3354(69443)

Question 1169119: On Monday morning, Mr. Descartes asked his Algebra students whether they had gone to the carnival in town over the weekend."did," said Kristen. "I went on the Teacups ride twice, the rollercoaster twice, and the Spinning Vortex once. I had a lot of fun for only $20. went on those rides, too!exclaimed Jorge. "Just once each on the Teacups and rollercoaster, but three times on the Spinning Vortex, all for $25.did five Teacup rides," said Lakesha. "And two rollercoaster rides, and one Spinning Vortex. I spent $29."Marc listed off the same rides. "Three Teacups for me, plus two rollercoasters , plus two rides on the Spinning Vortex, all for You don't need to say " interrupted Mr. Descartes , "I know how much you spent ." How much are the rides? How much did Marc spend? And how much is each ride?
Click here to see answer by Cromlix(4381)

Question 1170159: Consider the function T : Mnn → Mnn given by T (A) = tr(A)
Is T a linear operator? You must justify your answer.
Click here to see answer by ikleyn(52775)

Question 1170166: Let T : C[0,1] → R be given by
T(f) = f(0) + 3f′(0) + 2f′(1).
Is T one-to-one?
Click here to see answer by ikleyn(52775)

Question 1170165: Let D : P3 → P2 be the differentiation transformation D(p) = p′(x). Find the kernel of D.
Click here to see answer by ikleyn(52775)

Question 1170138: When you rent a car from Rental Agency A, for one day there is a base fee of
$20 and you pay $0.15 for each mile you drive. At Rental Agency B you pay a
base fee of $30 and get 100 miles free. Every mile after is $0.25 per mile.
1
Write a formula for the rental cost (C) in
terms of the miles (m) driven, for Agency A
and graph it.
2
Write a formula for the rental cost (D) in
terms of the miles (n) driven, for Agency B
and graph it.
3 What is the slope of the line from 100 miles
onward in the graph for Agency B?
4 Graph the formula for Agency A.
5 How many miles can you drive with $100,
Click here to see answer by Theo(13342)

Question 1170376: Will someone help me with this problem. I think it is A non-linear function that increases then decreases
The table below shows the relationship between the average number of hours students studied for a math test and their average grade.
Hrs Studied/ Average Grade
0 62
1 78
2 85
5 74
Which type of function is most likely to model this data set?

A linear function with a positive rate of change
A linear function with a negative rate of change
•
A non-linear function that decreases then increases
A non-linear function that increases then decreases

Click here to see answer by MathLover1(20849)

Question 1170703: Find a basis of the eigenspace associated with the eigenvalue −3 of the matrix A={-3,0,-3,-3},{0,-3,0,0}.{2,0,2,5},{-2,0,-2,-5}.
Click here to see answer by ikleyn(52775)

Question 1170701: The matrix A=({0,0,0},{0,3,-6},{0,3,-6}) has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace.
Click here to see answer by ikleyn(52775)

Question 1171569: Consider the following points.
(2013, 8), (2014, 9), (2015, 13)
(a) Determine the polynomial function of least degree whose graph passes through the given points.
p(x) =

(b) Sketch the graph of the polynomial function, showing the given points.
Click here to see answer by Alan3354(69443)

Question 1171641: 13-y=17 solve for y by dividing each side by -1
Click here to see answer by Boreal(15235)

Question 1171641: 13-y=17 solve for y by dividing each side by -1
Click here to see answer by Theo(13342)

Question 1172374: Find eigen value corresponds to eigne vector [3 2]t for M = [1 -3]
[-2 2]
Click here to see answer by ikleyn(52775)

Question 1172400: What are the eigen values of the follwong 3x3 matrix:
M = [3 5 3]
[1 7 3]
[1 2 8]
Click here to see answer by ikleyn(52775)

Question 1172394: If U and V are subspaces of a 7 dimensional vector space V, then what is the possible dimension of the intersection of U and V?
Click here to see answer by ikleyn(52775)

Question 1172552: Formulate a real-life problem involving linear inequalities in two variables then
solve.
Click here to see answer by ikleyn(52775)

Question 1172553: Graph the inequality y ≥ x + 1.
Click here to see answer by ikleyn(52775)

Question 1172551: The Cruz family went to an outing in a mountain resort. Mrs. Cruz gave to the
cashier Php1,000 bill for 2 adult tickets and 5 tickets for children that cost
more than Php700. Suppose an adult’s ticket costs Php 180.

a) What is the least price of each children’s ticket to the nearest peso?

b) The cost of each children’s ticket is Php125. Do you think that the money that Mrs. Cruz
gave to the cashier is enough? Why?
Click here to see answer by ikleyn(52775)

Question 1172803: Solve the system by the linear combination method, show all work carefully, show your answer, and check your answer.
x-2y=3
x+y=2(y+3)

Click here to see answer by ewatrrr(24785)

Question 1172814: 2x+3y=8. X-y=2

Click here to see answer by ewatrrr(24785)

Question 1173873: Thomas bakes pies for a local caterer. On Tuesday he made three peach pies and six cherry pies, costing him $48 in expenses. Friday he spent $54.50 to make seven peach and four cherry pies. What is the cost of each peach and each cherry pie?
Click here to see answer by greenestamps(13198)

Question 1174343: Q−1: [5×2 marks] Answer each of the following as True or False justifying your answers:
If A and B are n×n matrices, then 〖(A+B)〗^2=A^2+2AB+B^2.
If A is an n×n invertible symmetric matrix, then (A^(-1) )^k is symmetric, for any positive integer k.
Let A be an n×n matrix. If A is invertible, then |A|≠0.
If A and B are n×n matrices, then |A+B^T |=|A^T+B|.
The vectors (a,0,0), (1,a,0) and (2,3,a) in R^3 are linearly independent for all a∈R.

Click here to see answer by math_tutor2020(3816)

Question 1174361: On the first four exams, your grades are 76, 95, 56, and 77. There is still a final exam, and it counts as two grades. You are hoping to earn a C in the course. This will occur if the average of your six exam grades is greater than or equal to 70 and less than 80. What range of grades on the final exam will result in earning a C?
Click here to see answer by Boreal(15235)

Question 1174828: a trader buy some eggs at #15 she find that five of them are broken she sells the rest of #20 each and make a profit of #340 how many eggs did she buy
Click here to see answer by ikleyn(52775)

Question 1174832: the result of adding 15 to x and dividing the a same by 4 is the same as taking x from 80 a Express this statement as an algebra question B and find the value of x
Click here to see answer by greenestamps(13198)

Question 1175466: sketch the curve and find the area between curve and the x axis for the given bounds
a. y =x3+x2-2x between x=-3 and x=2
Click here to see answer by ewatrrr(24785)

Question 1175466: sketch the curve and find the area between curve and the x axis for the given bounds
a. y =x3+x2-2x between x=-3 and x=2
Click here to see answer by MathLover1(20849)

Question 1176400: Solve: 2a-3b+4x-a a=4 b=2 c=3

2.n(j+i)-k^5+n n=3 i=4 j=2 k=1

3.eg+2(f+e) e=2 f=0 g=5
Click here to see answer by greenestamps(13198)

Question 1176705: Please help me solve this question: Connor is playing a a card game called at Face Vaule. at the end of each round, players earn positive points for their remaining numbers cards but negative points for their face cards. at the end of round 1, connor earns -5 points. ant the end of round 2, he earns -6 points. what is Connors score now
Click here to see answer by Solver92311(821)

Question 1177729: Find the equation of the line passing through the point (−2,−7) and having an x-intercept of (67,0).
You may enter your equation in either the slope-intercept or point-slope form. Make sure to enclose fractions in parentheses, for example: y = (9/2)*x+(5/2).
Click here to see answer by josgarithmetic(39616)

Question 1177840: With the matrix A1∈M2,2(R) be defined A1 = [1/2//-1/-2] (sorry I don't know how to do properly matrices here in this platform)
What are his eigenvalues and eigenvectors associated with each eigenvalue of A1 ? And is the matrix A1 diagonalizable ?
Click here to see answer by ikleyn(52775)

Question 1178228: Solution to system of equations below and explain reasoning. f(x)= |x-4| + 2 and g(x) = 3x + 2
Click here to see answer by ikleyn(52775)

Question 1179331: Graph the line with slope 1 passing through the point, −5−1.
Click here to see answer by MathLover1(20849)

Question 1180398: add 3<=25-5<=125
Click here to see answer by ikleyn(52775)

Question 1180479: Consider the surface F(x,y,z)=x^6z^2+sin(y^6z^2)−8=0.
Find the following partial derivatives
∂z/∂x=
Mi answer is -((6xz)/(x^6y^6cos(y^6z^2))) but it's wrong.
∂z/∂y=
Mi anwer is -((6y^5zcos(y^6z^2))/(2x^6+2y^6cos(y^6z^2))) it's correct.
Click here to see answer by math_helper(2461)

Question 1180578: i have this question on matrix:
evaluate 1 1 1
a b c
a^2 b^2 c^2
Click here to see answer by ikleyn(52775)

Question 1180576: if A is the n*n matrix whose elements are all "a" and whose off diagonal elements are all "b" where a and b are any two real numbers, find the value of |A|
Click here to see answer by ikleyn(52775)

Question 1180650: Question 1 part a: Plot the line given that the equation of the line is y=x+1 and its domain is -2 B)State the coordinates of the x and y intercept if there is any.
Question 2: Plot the graph y=x and state the coordinates of the x and y intercept when the domain is -3
Click here to see answer by ikleyn(52775)

Question 1180649: how to solve linear equations Plot the line given that the equation of the line is y=x+1 and its domain is -2
Click here to see answer by ikleyn(52775)

Question 1180762: There are 120 deer in a forest. The population of the deer doubles every 5 years. How long would it take for the deer population to reach 3840?
Options:
25 years
50 years
5 years
35 years
Click here to see answer by josgarithmetic(39616)

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