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

Tutors Answer Your Questions about Linear Algebra (FREE)

Question 60693: Can you help me solve this, I need to graph it? f(x) =2/5x
Click here to see answer by Earlsdon(6287)

Question 60982: Another slope that I have trouble with. CAn anyone give me a hand? Thanks!
Write the equation of the line that passes through (0,3) and is parallel to
3y = x +10.
Thanks again for your efforts!
Click here to see answer by joyofmath(189)

Question 60981: This is a two part question. Can anyone help me set these up. I seem to have issues with these slopes. Thanks!
Using point P(2,9) and Q (-3,3)
Find distance between P and Q.
Find the equation of the line passing through P and Q.
Thanks again!
Click here to see answer by joyofmath(189)

Question 60979: I am not sure where to start...can anyone help me?
Graph the line:
x - 2y = 2
Thanks for your help.
Click here to see answer by jainenderkapoor(61)

Question 61084: I need to find the basis for the null space, the range of the matrix, and the orthogonal basis using Gram-Schmidt.
The matrix is:
1 -2 1 -5
2 1 7 5
1 -1 2 -2
Click here to see answer by venugopalramana(3286)

Question 61169: Can you give me a hand with this one? Thanks!
x/x-2 = 2/x-3 Solve for x
thanks!
Click here to see answer by jai_kos(139)

Question 61865: x + 5y = 7
Click here to see answer by rchill(405)

Question 61902: Hi you guys, i need help with this question for sat or sunday, thank you very much.

Find the distance from the point Q(-3,-3,-4) to the line which passes through the point P(3,3,-4) and is parallel to the line whose equation is:
(x,y,z) = (-7,1,-2) + t(-1,-2,2).

Click here to see answer by venugopalramana(3286)

Question 62053: Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour than Smith, and his trip took 1/2 hour longer than Smith's. How fast was each one traveling?
Click here to see answer by uma(370)

Question 62609: Consider the linear transformation T : R3 -> R2 whose matrix
with respect to the standard bases is given by
2 1 0
0 2 -1

Now consider the bases:
f1= (2, 4, 0)
f2= (1, 0, 1)
f3= (0, 3, 0) of R3 and
g1= (1, 1)
g2= (1,−1) of R2
Compute the coordinate transformation matrices between the standard
bases and these bases and compute the matrix of T with respect to the new
bases.
Any help would be appreciated. Thank you!
Click here to see answer by venugopalramana(3286)

Question 62451: Find the shortest distance between the two lines:
(x,y,z) = (2,-1,2) + t(-3,-2,-2)
(x,y,z) = (-3,4,1) + s(0,2,0)

Thanks sooo much!

Click here to see answer by venugopalramana(3286)

Question 62447: Find the shortest distance between the plane 2x+4y-2z=6 and the line (x,y,z) = (-1,-2,4) + t(-2,-1,-4).
Distance =????
Thank you!
Click here to see answer by venugopalramana(3286)

Question 62449: Find the point P on the plane 0x+1y-3z=8 closest to the point Q(2,-3,3).
P = ( , , )?????
Thank you guys!

Click here to see answer by venugopalramana(3286)

Question 62805: Hi,my name is Natalia. I solved two problems, but I'm not sure that I did it right. I would really appreciate if you can check them.
Here are two given problem:
Consider a vector space V=Mat 3x3 of all 3x3 matrices
Q.: determine the dimension of V,find and verify a basis for it.
here is what i've got so far:
if the matrix is
/a b c/
/d e f/
/g h i/
then the basis for it is
/1 0 0/ /0 1 0/ /0 0 1/ /0 0 0/ /0 0 0/ /0 0 0/ /0 0 0/ /0 0 0/ /0 0 0/
/0 0 0/,/0 0 0/,/0 0 0/,/1 0 0/,/0 1 0/,/0 0 1/,/0 0 0/,/0 0 0/,/0 0 0/
/0 0 0/ /0 0 0/ /0 0 0/ /0 0 0/ /0 0 0/ /0 0 0/ /1 0 0/ /0 1 0/ /0 0 1/
So, i have 9 vectors v1, v2,...,v9 that are lineraly independent and span
therefore, dimV=9 if the matrix is symmetric dimV=6 and if the matrix is scew-symmetric dimV=9 Am I correct?
And the second problem:
A have a matrix A=
/1 2 3 /
/2 5 7 /
/3 7 10/
that lookes like A=
/1 0 1/
/0 1 1/
/0 0 0/ when row-reduced

I need to express a vector x=
/2 /
/-1/
/7 /
as a sum of a vector from the row space and a vector from nullspace
For nullspace I got (let's call it v so it will be easier to write an expression then)
/-1/
/-1/
/1 /
for row space (u and w respectively)
/1/ /0/
/0/ /1/
/1/ /1/
that gives me 3-D subspace
and the vector expression is:
x=2*v + 4*u + 1*w
did I solve it correct?
Thank you very much!
Click here to see answer by venugopalramana(3286)

Question 62943:
Click here to see answer by funmath(2925)

Question 62946: The following table shows data for the city K that consist of i ts population during the time period from the year 1942 to the year 2002.
Scatter plotting
1940- 20,360
1950- 23,390
1960- 28,580
1970- 35,425
1980- 45,260
1990- 54,320
2000- 63,525
Find a qudratic model for the data.Round the values of a,b,and c to three significant digits?
Click here to see answer by stanbon(57214)

Question 63391: Please give me the workings of x^2-x-6/2x^2-13x+21
Click here to see answer by ankor@dixie-net.com(15622)

Question 63918: with a tail wind, a helicopter traveled 300mi in an hour and 40 min. the return trip aganst the same wind took 20 min longer. find the wind speed and also the air speed of the helicopter.
Click here to see answer by funmath(2925)

Question 63991: I tried this problem and did not understand my answer. i would put in my work but some of the terms i need like a fraction line are not on my computer
.5(6-z)=z
Click here to see answer by sarahschober(35)

Question 64548: Solve. Approximate to four decimal places.
4^(3x+2)=9
Click here to see answer by ankor@dixie-net.com(15622)

Question 64551: Find the midpoint of the line segment between (-3,-4) and (6,-8)
Click here to see answer by stanbon(57214)

Question 64547: ((3x^2-12)/(x^2=2x-8)) / ((6x+18)/(x=4))
Click here to see answer by stanbon(57214)

Question 64552: Solve for x: [6x-5]-3=-2
Click here to see answer by checkley71(8403)

Question 64546: (5a-2)^2-a=0
Click here to see answer by checkley71(8403)

Question 64875: write an equation in slope intercept form for the line passing through each pair of points
1. (-1,3) and (2,-5)

Click here to see answer by Edwin McCravy(8879)

Question 64945: Bette’s Bananas delivers fresh bananas to your doorstep every morning. The cost for the service is $12/month flat rate and your first ten bananas are free! Further bananas cost $0.10 each. Construct a piecewise-linear function for the cost C of receiving N bananas in a month.
Click here to see answer by stanbon(57214)

Question 65314: 2x+3y=1
-3x+4y=-10
Click here to see answer by checkley71(8403)

Question 65068: how do you graph
4x>12
2y<6
Click here to see answer by checkley71(8403)

Question 64665: What is the Graphical Method?
Click here to see answer by checkley71(8403)

Question 64649: Can anyone give me a hand with this one? Thanks!
3^x-1 = 2
Give answer to four decimal places. Thanks again!
Click here to see answer by Earlsdon(6287)

Question 65750: determine the ratio in which the line joining (0,7) and (-2,1)is
divided by the line 2x+y-4=0
Click here to see answer by Nate(3500)

Question 65750: determine the ratio in which the line joining (0,7) and (-2,1)is
divided by the line 2x+y-4=0
Click here to see answer by Edwin McCravy(8879)

Question 65752: what point on the y axsis is equidistance from P(0,8) and Q(-4,4)
Click here to see answer by tanimachatterjee(60)

Question 65751: if A(x,y) is equidistance from P(-3,2)and Q(2,-3), show that x =y
Click here to see answer by venugopalramana(3286)

Question 65749: the line joining A(2,3) and B(6,-5)meet the xaxis at P .
write down the y cordinate of P hence find the ratio AP:PB
Click here to see answer by stanbon(57214)

Question 65862: if (6t+7a)/4=t, then what is 4t in terms of a?
the answer is -14a i would like to know how to get that answer.
thank you
Click here to see answer by josmiceli(9645)

Question 65959: There are 850 Douglas fir and ponderosa pine trees in a
section of forest bought by Sawz Logging Co. The company paid an average of
$300 for each Douglas fir and $225 for each ponderosa pine. If the company paid
$217,500 for the trees, how many of each kind did the company buy?
Click here to see answer by stanbon(57214)

Question 65955: 3x - 5(3x - 7) = 2(x + 9) + 45
3x-15x-35=2x+18+45
-12x-35=2x+63
(-12x-35)+35=2x+63+35
-12x =2x+98
-12x-2x=2x+98-2x
-10x=98
-10x/-10=98/-10
x=-9 8/10 or -9 4/5
Click here to see answer by shermalaine(1)

Question 65958: A bus leaves a station at 1 P.M., traveling west at an aver-age
rate of 44 mi/h. One hour later a second bus leaves the same station, traveling
east at a rate of 48 mi/h. At what time will the two buses be 274 mi apart?
Click here to see answer by chitra(359)

Question 65954: 2(x -3) - 3(x + 5) = 3(x - 2) - 7
Click here to see answer by chitra(359)

Question 65979: The length of a rectangular playing field is 5 ft less than twice its width.
If the perimeter of the playing field is 230 ft, find the length and width of the field

Click here to see answer by uma(370)

Question 65996: A common mistake when solving equations is the following:
The equation: 2(x -2) = x +3
First step in solving: 2x -2 =x +3

Write a clear explanation of what error has been made. What could be done to avoid this error?

Click here to see answer by uma(370)

Question 66018: How do you multiply this set of matrices? [5 4 8] _\/ {-8 6} [3 -4 -2] ^/\ { 0 -2} The first matrix is a 2x3 and the second one is a 2x2.

Click here to see answer by Edwin McCravy(8879)

Question 66010: Solve the following system of equations algebraically:
9x^2 + y^2 = 9
3x – y = 3
Click here to see answer by Edwin McCravy(8879)

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