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

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 Algebra: Linear Algebra (NOT Linear Equations) Solvers Lessons Answers archive Quiz In Depth

 Question 356729: What is a subspace ? How do you prove that it is a subspace ? I know that it is a straight line or plane that passes through the origin. But the proof of a subspace of 3 rules seems too basic. It almost allows all vectors to be subspaces. I have not seen a vector that is not a subspace yet. the rules are something like multiply by 0 addition of u and v scalars multiplication by scalars. My assignment question reads W is the space of all vectors of the form (x, y, x-y) Find out if W is a subspace. JUstify your answer. I need the answer put in basic english, with as much detail as possible. The question somehow is worth 10% of assignment, and to me it seems to basic. I just have problem with the wording. Can anyone help with expressing this answer in clear English. Thank You Click here to see answer by robertb(4012)

 Question 357740: Tickets for your school's play are \$3 for students and \$5 for non-students. On opening night 937 tickets are sold and \$3943 is collected. How many tickets were sold to students? to non-students? Click here to see answer by nyc_function(2733)

 Question 357809: OK, I have spent every waking second trying to figure this out. d=sqrt(2h) I made my height easy, 6 mile, or 30,680 feet. I know R stands for the radius of the Earth which is approximately 3,960 miles. This is what I have come up with...not good, but it's all I have: (r+h)^2=r^2+d^2 simplifying (r+h)^2 i get r^2+2rh+h^2=r^2+d^2 I need to move r^2 to get d^2 alone so I now have 2rh+h^2=d^2 now to get d standing completely alone I have to radical both sides? ([square root]2hr+h^2)=d ?? Then I just plug in my numbers and get it. But i keep coming up with a ridiculous number like...d=47556miles. The closest I have gotten to a reasonable answer is 3,966 miles and thats my total sum of r and h, so i know thats wrong. Ok here's my question. I'm in a plan, 6 miles in the air, what's the distance that I should be able to see the horizon using d=sqrt(2h)? I'm so lost. Please and THANK YOU!!!! Click here to see answer by ankor@dixie-net.com(15638)

 Question 358097: During one calendar year a state trooper issued a total of 375 citations for warnings and speeding tickets.Of these there were 37 more warnings than speeding tickets.How many warnings and how many speeding tickets were issued? Click here to see answer by solver91311(16868)

 Question 358398: Solve the following initial value problems: A)x"+x=0 :x(0)=0,x'(0)=1 b)x"+4x=0; x(0)=1, x'(0)=0 Click here to see answer by robertb(4012)

 Question 358553: Find the equation of the parabola passing through the given points (1,3)(2,3)(3,5). Show the system of equations containing the 3 points and then solve for the constants, a,b,and c. Then, show the standard form equation of the parabola. Click here to see answer by ewatrrr(10682)
 Question 358553: Find the equation of the parabola passing through the given points (1,3)(2,3)(3,5). Show the system of equations containing the 3 points and then solve for the constants, a,b,and c. Then, show the standard form equation of the parabola. Click here to see answer by Alan3354(30983)
 Question 358553: Find the equation of the parabola passing through the given points (1,3)(2,3)(3,5). Show the system of equations containing the 3 points and then solve for the constants, a,b,and c. Then, show the standard form equation of the parabola. Click here to see answer by Fombitz(13828)

 Question 358837: Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 15 gallons of fuel, the airplane weighs 2187 pounds. When carrying 35 gallons of fuel, it weighs 2303 pounds. How much does the airplane weigh if it is carrying 50 gallons of fuel? Click here to see answer by stanbon(57246)

 Question 358930: a gym offers two options for membership plans. option A includes an initiation fee of \$121 and costs \$1 per day. option B has no initiation fee but costs \$12 per day. after how many days will the total costs of the gym membership plans be equal? how does your answer change if the daily cost of option B increases? Click here to see answer by mananth(12270)

 Question 358851: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 11 hours of burning, a candle has a height of 23.4 centimeters. After 30 hours of burning, its height is 12 centimeters. What is the height of the candle after 13 hours? Click here to see answer by ankor@dixie-net.com(15638)

 Question 358679: solve Linear sestems when w=1 w+2x+2y+z=-2 w+3x-2y-z=-6 -2w-x+3y+3z=6 w+4x+y+2z=-14 think you Click here to see answer by Fombitz(13828)

 Question 359720: This is a very simple question and it's embarassing to ask. I am being thrown off by the omition of a variable. Given the piecewise defined function y={-2 if x=0, find f(0) Is this a trick question since there is not a variable accompanying the -2? It seems like it should state y={-2x if x=0, find f(0) Click here to see answer by Fombitz(13828)

 Question 360105: A truck can be rented from Basic Rental for \$50 per day In addition you pay 20 cent per mile. Continental charges per day \$20 per day in addition to 50 Cent per mile rent out the same truck. How many miles must you drive in a day to make the cost for Basic Rental a better deal than that Continental? Click here to see answer by mananth(12270)

 Question 360120: You need to choose between two telephone plans foor local calls. Plan A charges \$25 month for unlimited calls. Plan B charges a monthly fee of \$13 with a charge of \$0.06 per local call. How many local telephone calls in a month make Plan A the better deal Click here to see answer by ewatrrr(10682)

 Question 360199: For each line use the given conditions to write an equation in the point-slope form first and then rearrange the values into the slope-intercept form. l. Slope=4, passing through(1,3) ll. Slope= 8, passing through (4,-1) lll. Slope= -5 passing through(-4,-2) lv. Slope= -2, passing through (0,-3) Click here to see answer by solver91311(16868)

 Question 360576: John has some dimes and quarters in his pocket. The value of the coins are \$6.20. There are 8 more quarters than dimes. How many dimes and quarters does he have? Please help on the equation set up. Thanks! Click here to see answer by scott8148(6628)

 Question 39572: Proof of a singular matrix: I need to show (in general) that either matrix A is "singular" or "A^2 = A^(-1)". A is an n*n square matrix such that A^4 = A. I want to know how to do this problem and what happens if the exponent values are different.(for example, odd number exponents?) Click here to see answer by robertb(4012)

 Question 362367: I wanted to know how to solve by graphing. -3x-y=-10 4x-4y=8 (-1,3)or (1,3) or (3,-1) or (3,1) I forgot how to solve and I have finals this week... Thanks for any help... Angelia Click here to see answer by mananth(12270)

 Question 362544: Solve the equation. Be sure to check your proposed solution by substituting for the variable in the original equation. 12(z+3)-4(z-1)=3(z-2)+4(z-1) A. the solution set is { } B. The solution set is all real numbers C. The solution is an empty set Click here to see answer by ghali0079(12)

 Question 363034: Are the points (-1,8), (1,2), and (4,-7) on the same line? Explain your reasoning Click here to see answer by mananth(12270)
 Question 363034: Are the points (-1,8), (1,2), and (4,-7) on the same line? Explain your reasoning Click here to see answer by Edwin McCravy(8882)

 Question 363033: Find the value of k if the line through the points (k+1, k-2) and (3,4) is parallel to the line through the points (3,1) and (6,-1). Click here to see answer by mananth(12270)

 Question 362877: solve the matrix equation AX=B for the 2x2 matrix X: A 2 -7 -1 4 ] x= B -21 3 12 -2 Click here to see answer by Fombitz(13828)

 Question 363035: The variable y varies directly as the square of x, and y=2 when x=2. Write an equation that relates x and y. Find y when x=1.5. Click here to see answer by ewatrrr(10682)

 Question 362946: A jet flew 1200 miles with a tailwind of 50 mph. The tailwind changed to 20 mph for the remaining 520 miles of the flight. The total time of the flight was 3 hours. Find the speed of the jet relative to the ground. Please help me out here, and if you dont mind including the step by step process that would be great! Click here to see answer by checkley77(12569)

 Question 363036: A line passes through the points (k=3,-2k) and (4,1) and has a y-intercept of 6. Find the value of k. Click here to see answer by ankor@dixie-net.com(15638)