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...
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...
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...
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...
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...
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...
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...
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...
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...
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!
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...
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...