Tutors Answer Your Questions about Linear Algebra (FREE)
Question 15391: Suppose V is an n dimensional vector space and that T is an operator on V. T has n distinct eigenvalues. Also suppose that S is also an operator on V which has the same eigenvectors as T ( not necessarily with the same eigenvalues).
Prove that ST = TS
Click here to see answer by khwang(438)  |
Question 16274: this is a four answer question. I found one of the answers by just guessing but I don't know how the operations work on a problem like this so can someone please eplain this to me?  enter them in increasing order: x1= __ x2= __ x3= __ x4=3
Click here to see answer by Earlsdon(6287) |
Question 16274: this is a four answer question. I found one of the answers by just guessing but I don't know how the operations work on a problem like this so can someone please eplain this to me? enter them in increasing order: x1= __ x2= __ x3= __ x4=3
Click here to see answer by tjnw79(57) |
Question 17949: I have been working on trying to find the eigenvalues and eigenvectors of the following matrix:
3 -1 2
2 0 2
5 -1 0
I have worked it to the point of finding the characteristic polynomial of:
-Lambda^3 + 3*Lambda^2 + 10*Lambda -8
This doesn't seem correct to me since, MATLAB gives the eigenvalues of (4,-2,1).
That is where I am stuck.
Any help is greatly appreciated.
Click here to see answer by venugopalramana(3286) |
Question 18656: ABCD is a sqaure. The midpoints of BC and CD are M and N respectively.
a) Express vector AM and vector An as linear combinations of vector AB and vector AD.
b) Express vector AB and vector AD as linear combinations of vector AM and vector AN.
Click here to see answer by venugopalramana(3286) |
Question 18994: is the following a linear transformation from R^3 to R^2?
L(x1,x2,x3) = (x2-x3,x1+2) ?
so i know how to prove that this is not closed under scalar multiplication and addition (due to the "2" in the second entry). so then is my answer just "no, it is not a linear transformation from R^3 to R^2 because it is not closed under scalar multiplication." ?
what about linear transformation from R^3 to R^4: L(x1,x2,x3) = (x2-x3,x1*x2,2x2-x1,x3+x2) ?
for this one, i dont quite understand how to go about it because the second entry is a product of two numbers and not just a sum. so then whould it count as being closed under scalar multiplication and addition? plus i remember seeing somewhere if R^m ---> R^n, then m must be greater than or equal to n. so then by this rule, the answer is automatically no because we are going from R^3 to R^4 and (obviously) 4 is greater than 3. i'm just not sure about all of this...
thank you so much for your help : ) i greatly appreciate it!!!
Click here to see answer by khwang(438) |
Question 20750: Hi, I'm in homeschooling and I'm having trouble with matrices. I was wondering how to solve the problem where you have to find the x,y, and z values in the matrix:
[7 -7 5 | 9]
[9 5 -7 | -17]
[6 1 -7 | -2]
I'd appreciate the help. Thank you!
Caitlyn Reese
Click here to see answer by venugopalramana(3286) |
Question 20219: question:you need 12 gallons of water for your garden. if you only have two buckets, one that holds 4 gallons and one that holds 9, how can you bring the water in only one trip?
my answer:
gallons, less than or equal to, 12
gallons, less than or equal to, 4
gallons, less than or equal to, 9
9+4=13
4 gallons in one and 8 gallons in the other
would this answer be correct?
Click here to see answer by danielle123(2) |
Question 20758: Recall that P3 is the space of all polynomials of degree less than three with real coefficients. Define an inner product < , > on P3 given by:
< p,q > = the sum from i=1 to 3 of p(i-1)*q(i-1), and let || || be the norm with respect to this inner product.
(a) let p(x)=1+x-x^2 and q(x)=2-x
Find a polynomial f(x) in P3 which is orthogonal to both p(x) and q(x) with respect to the inner product.
(b) find the distance between p(x)+q(x) and f(x).
thank you so much for your help!
Click here to see answer by khwang(438) |
Question 20562: I have a homework question where it asks the following question:
Find the standard matrix representation for the following linear transformation. L is the linear transformation that rotates each xER^2 (every x in R^2) by 45 degrees in the counterclockwise direction then reflects about the line x2=x1.
So far, I drew the geometric representation of the problem, where e1 is rotated from x1-axis and e2 is rotated from x2-axis by 45 degrees. Where I am is the 'relfects about the line x2=x1.' I have no idea what to do from here, can you help me?
Click here to see answer by khwang(438) |
Question 21046: Matrices with the property A*A=AA* are said to be normal.
1. Verify that symmetric matrices and hermitian matrices are normal.
2. Give and example of a 2x2 matrix which is not symmetric nor hermitian but normal
3. Prove that if A is normal, then R(A) _|_ N(A).
Click here to see answer by venugopalramana(3286) |
Question 21096: Hi! I'm in homeschooling and I've been having trouble with matrices. I asked a question the other day about them, and I'm still having trouble with another problem on my lesson. I'd appreciate the help!
Here's the matrix:
[ 7 -4 -2 | 9 ]
[-5 8 5 |-8 ]
[-5 5 8 |-2 ]
Thank you!
Caitlyn
Click here to see answer by venugopalramana(3286) |
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