Tutors Answer Your Questions about Linear Algebra (FREE)
Question 24971: Factor completely:
1) y³ - 3y² - 4y + 12
2) 2x³ + 6x² - 8x - 24
Factor:
1)6(2p+q)²-5(2P+q)-25=
Factor. Assume that variables in exponents represent natural numbers.
1) 25y2m - (x2n-2xn+1)
2) x6a - t3b
3) (y-1)4 - (y-1)
4) X6 - 2X5 + X4 - X2 + 2X - 1
Click here to see answer by AnlytcPhil(1806)   |
Question 24998: 1. Is √x ^2 = x an identity (true for all values of x)?
Explain the answer
2. For the equation x - √x = 0 perform the following
a. Solve for all values of x that satisfies the equation.
b. graph the functions y = x and y = √ x on the same graph (by plotting points)
How does the graph relate to part a?
Click here to see answer by stanbon(75887) |
Question 25057: Hello:The question is:
Find values of a, b, and c such that the graph of the polynomial p(x) = (ax^2) + bx + c passes through the point (-1,0) and has a horizontal tangent at (2, -9)
What I did first was substitute (-1, 0) into p(x): a4 + b2 + c = -9
Then I took the first derivative of p(x) and got: 2ax+b.
This is were I'm stuck. I believe I should use this for a second equation, then set up a matrix and solve for a,b and c, but I'm not sure.
Thanks
Click here to see answer by stanbon(75887) |
Question 25058: Hello:
I am not sure how to answer this question.
If A and B are nxn matrices, then show that there are no square matrices A and B such that AB-BA=I
(where I is the Identity).
I know that if AB = I and BA = I then AB-BA cannot equal I. Sorry I am confused.
Thanks
Click here to see answer by kev82(151) |
Question 25255: When using gaussian elimination, can an inconsistant solution have a general solution? i worked out the matrix and came to a spot where 1=-3 and 1=10.4 (inconsistant 1 can't equal 2 different solutions); would there still be a way to formulate a general solution such as x=(2-4x,2-3x,x,0) = (2,2,0,0) + x(-4,-3,1,0)
I hope this is enough information to clearly explain my question. thanks
Click here to see answer by venugopalramana(3286) |
Question 25312: 1.At the high school band's annual spaghetti dinner, the members served 210 dinners and collected $935. The band leader did not designate which ticket was an adult or child dinner. You need to know that to prepare the correct amount of food and for future planning. Each adult dinner cost $6 and each child's dinner cost $3.50.
Let a = number of adult dinners
Let c = number of child dinners
Write two equations to represent the total amount raised from the dinner and the total
2.2. Use substitution to solve the above system of equations. How many adult dinners were sold and how many child dinners were sold?
Show all your work to receive full credit for this problem.
Click here to see answer by Paul(988) |
Question 24118: The cost of sending an overnight package from speedy air is $15.00 for the first pound and 3.00 for each additional pound. How much will it cost to send a 7 pound package? it is telling you to assign labels to the parts of the verbal model, use the labels to translate the verbal model into an algebraic model then solve the model..ive done the first step but the rest is throwing me completely off could you please help me?? thanks a million!
Click here to see answer by stanbon(75887) |
Question 25850: I'm just stuck on this easy question. I know I just use the LCD; but I keep getting stuck.
(x +1) + (x+2)=2 The (x+1) is over 3 and the (x+2) is over 7, so they are two fractions being added but I couldn't get it to look right on this screen.
I have tried multiplying the whole equation by 21; isn' that correct? i need some help.
Click here to see answer by elima(1433) |
Question 26364: Consider the accompanying matrix. Use the test for linear independence to find a basis for the space spanned by the rows of the matrix. Suppose that this matrix is augmented matrix for a system of equations. What is the rank of this systen? Which equations can be discarded?
{[1 0 1 1
2 1 3 0
3 3 6 -3
4 1 5 2]}
Click here to see answer by venugopalramana(3286) |
Question 26495: I have a homework problem that I don't know how to do.
I'm asked to solve the following problem;
For what values of h is v3 in span {v1,v2} and for what values of h is {v1,v2,v3}linearly dependent?
given that
----[ 1]-----[-2]------[ 2]
v1=[-5]-v2=[10]--v3=[-9]
----[-3]-----[ 6]-------[ h]
Click here to see answer by venugopalramana(3286) |
Question 27159: I have a few questions on solving linear equations. We must use method's 1-graphing, method's 2-substitution, method 3/4- solving with elimination.
here is a questions using method 4:
x+2y=6
5x+3y=2
here is my work-?
1x+2y=6
5x+3y=2
5(1x+2y=6)
1(5x+3y=2)
5x+10y=30
5x+3y=2
13y=32
13 13
y=2.46?
x+2(2.46)=6
1x+4.92=6
-4.92 -4.92
x=1.08?
(1.08,2.46)???
Click here to see answer by bmauger(101) |
Question 27388: Determine whether the following functions T : V -> W define linear transformations
(be sure to justify your answer fully):
V = W = P(Rational), T(f)(x) = (x + 1)f(x) − f(1)x^2.
Thanks a lot to who ever is solving this. Means a great deal.
Thank you.
Click here to see answer by khwang(438) |
Question 27385: Let V = matrix M(2×2)(Complex). Let W1 = {A = (Ajk) 1 <=j,k<=2 exists in V | A11 + A22 = 0 }.
a) Find subspaces W2 and W3 of V such that
V = W1 + W2, V = W1 + W3, W2 not equal to W3.
(Note: One way to describe a subspace is to give a basis for it.)
b) Explain why W2 (intersect) W3 = {0} for any pair of subspaces W2 and W3 satisfying the
conditions of part a).
Click here to see answer by khwang(438) |
Question 27384: Let V = P3(Q) and W = { f(x) 2 V | f(x) = f(−x + 1) }. Find a basis for W.
Let V and W be same as above. Find a basis for V that contains a basis for W.
I am totally confused. I really need some help here.
Thanks.
Click here to see answer by khwang(438) |
Question 27581: I have a Radius of 2mm, but i dont have the coordinate for that circle.
I also have a point of intersection of the tangencey of the circle,I know X, and Y coordinate for this location,
I would like to find out how can i find the distance from the center of the cirle to the point of tangency.
Or find the location of the center of cirle,
the Coordinate for the point of tangency are
X=12 (
y=201.8
Click here to see answer by venugopalramana(3286) |
Question 27273: Hi-I'm having troubles with a problem that is based on Mathematica. This problem deals with vectors and linear dependency. Here is what the problem is asking: Below is the table that describes the composition of the three basic mixtures of concrete, Type S, Type A, and Type L. The corresponding vectors for these mixtures and for two custom mixtures, Type U and Type V, have been entered below.
Super-Strong All-Purpose Long-Life
Type S Type A Type L
Cement 20 18 12
Water 10 10 10
Sand 20 25 15
Gravel 10 5 15
Fly Ash 0 2 8
Type U Type V
Cement 12 15
Water 12 10
Sand 12 20
Gravel 12 10
Fly Ash 12 5
(a) Show that {S,A,L} is a linearly independent set of vectors. What practical advantage does that have?
(b) Show that we can make the custom mix V but not the custom mix U from the three basic mixes S,A,L. What does this say about the linear independence of the sets {S,A,L,U} and {S,A,L,V}?
(c) Explain why any combination of S,A,L,and V can also be achieved by a combination of just S,A and L. For example, show how to make the custom mix 3S+4A+2L+3V using only S, A, and L.
(d) Define a fifth basic mix W to add to {S,A,L,U} such that any custom mixture can be expressed as a linear combination of the set of mixes {S,A,L,U,W}.
(e) Why will there still be mixes that cannot be physically produced from this set of five basic mixes? (Hint: Consider the signs of the scalar weights.) Give an example of such a mix.
I've got parts (a),(b), and (c) figured out but parts (d) and (e) I'm confused about.
On part (d) I added the four vectors {S,A,L,U} together to get W. After that I put the vectors {S,A,L,U,W,{0,0,0,0,0}} into a matrix and solved for the system. As the solution set shows I get {-c5,-c5,-c5,-c5,c5} for my scalar weights. I set c5=1 and get the linear dependence relation: -S-A-L-U+W=0. I thought this was the right method to define W, but then I realized that you cannot have negative values for the mixes.
Because I cannot get part (d) I'm having a lot of trouble answering part (e). Is there a clearer explanation for the question being asked in part (e)?
If you could help me out with this problem I will greatly appreciate it. Thank you so much for taking the time to help.
Click here to see answer by venugopalramana(3286) |
Question 27855: 1. calculate the slope and midpoint of ( -1 , 7 ), ( 1 , 5 )
2. calculate the slope and midpoint of ( 8.2 , 6.9 ), ( -20.1 , -8.2 )
3. calculate the slope and midpoint of ( -8.4 , 6.9 ), ( -8.5 , 5.1 )
4. calculate the slope and midpoint of ( -34 , -41 ), ( -26 , 42 )
5. calculate the slope and midpoint of ( -7 , 8 ), ( -4 , -3 )
6. calculate the slope and midpoint of ( -25.7 , -16.2 ), ( -40.6 , 12.2 )
7. calculate the slope and midpoint of ( 12 , 1 ), ( 36 , -42 )
8. calculate the slope and midpoint of ( -1 , -8 ), ( -7 , -4 )
9. calculate the slope and midpoint of ( 2.1 , 3.8 ), ( 3.1 , 7.6 )
10.calculate the slope and midpoint of (41.8 , -18.2 ), ( 18.6 , 0.8 )
Click here to see answer by bmauger(101) |
Question 28551: A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Identify 2 points that satisfy the inequalities.
Click here to see answer by stanbon(75887) |
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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
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