Recent content by lubricarret

1. Diagonalizable matrices

Thanks HallsofIvy! I appreciate the explanation and for assuring me of that proof!!
2. Diagonalizable matrices

Homework Statement Let A and B be diagonalizable 2 x 2 matrices. If every eigenvector of A is an eigenvector of B show that AB = BA. Homework Equations D = PA(P^-1) The Attempt at a Solution Since the eigenvectors are equivalent, wouldn't it hold true that P_A = P_B? If I have...
3. Inverse Matrix Question

Thanks again Dick for clearing this up for me!
4. Inverse Matrix Question

Homework Statement Let A be an invertible 3x3 matrix. Suppose it is known that: A = [u v w 3 3 -2 x y z] and that adj(A) = [a 3 b -1 1 2 c -2 d] Find det(A) (answer without any unknown variables) Homework Equations The Attempt at a Solution I found A^(-1) to be equal...
5. Composite Matrix Transformation - Reflection

Hi, Thanks again HallsofIvy. I used the unit vectors in my formula, and it seems to come out with the same answer; except I tried the technique you gave and I still come up with [(-7/25) (24/25) (24/25) (7/25)] for the second Matrix. I guess I'm making some calculation error, as...
6. Closest possible points on skew lines

Thanks for the reply Dick! Ahh k, got it now!! )
7. Composite Matrix Transformation - Reflection

Homework Statement Let T1 be the reflection about the line 2x–5y=0 and T2 be the reflection about the line –4x+3y=0 in the euclidean plane. (i) The standard matrix of T1 o T2 is: ? Thus T1 o T2 is a counterclockwise rotation about the origin by an angle of _ radians? (ii) The...
8. Closest possible points on skew lines

Homework Statement Find points P,Q which are closest possible with P lying on line: x=7-5t, y=-5+11t, z=-3-1t and Q lying on line: x=-354-8t, y=-194+12t, z=-73+7t *the line joining P + Q is perpendicular to the two given lines. Homework Equations Projection formula, cross...
9. Matrix Diagonalizable Question

Ahhh, Okay. I don't know why I didn't see that before... obviously then, there are two parameters for the 0 matrix, which would make it invertible... the parameters there would be t[1,0] and s[0,1] (or as you said any vector <x, y>. And thanks Dick, I see that when you have a k value other than...
10. Matrix Diagonalizable Question

Hi Dick, Thanks a lot for the help! The question was only asking for which k values, so your explanation of k=0 for the first one solved my mistake. But, if you could just clear something up for me that I don't really understand: As you mention the first one is diagonalizable if k=0, to...
11. Matrix Diagonalizable Question

Homework Statement 1. Let A = [-8 k 0 -8] Then A is diagonalizable exactly for the following values of k 2. Let B = [-8 k 0 1] Then B is diagonalizable exactly for the following values of k Homework Equations -Equations for eigenvalues, eigenvectors... and D=PA(P^-1) -A...
12. Distance between two parallel lines

Aa! Can't believe I made such a stupid mistake. Thanks!! So, the answer would just be (5/33)(sqrt33), correct?... As I would keep P as (0,0,-1), but make A (0,0,-6); and get the vector AP = (0,0,5) So, projecting AP onto the normal, and then getting the distance of the projection would...
13. Linear Algebra; AB=AC

Great, thanks guys! I set each to equal the zero matrix; so ended up getting a = 4c, and b = 4d. I used arbitrary numbers for C and D, and got two separate matrices B and C such that AB = AC... for example, these worked out: [4 8 1 2] and [12 16 3 4] Thanks for clearing that up for me!
14. Distance between two parallel lines

Homework Statement Determine the distance between the parallel planes –4x–4y+1z=–1 and 8x+8y–2z=12 Homework Equations Proj_n_v = ((vn)/(nn))n The Attempt at a Solution I thought I understood how to do this, but I am not getting a correct answer for it. What I did was: I made the...
15. Linear Algebra; AB=AC

Thanks for the help! This may sound like a stupid question, as I've encountered this problem before in this course... how would I solve for 4 unknowns in this way; I haven't taken Math for 4 years before Linear Algebra, so I'm rusty on how to do these types of equations. I would set all...