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Jake204598

Guest

Linear Algebra

I was wondering if anyone could help me with some liners algebra problems?
1.Let T = (tij ) be the 7 ×7 matrix with (i, j)-entry tij given by
ti,i+1 = 1, 1 ≤i ≤6, tij = 0 for all other i, j.
Is the collection of matrices
{T, T 2, T 3, T 4, T 5, T 6}
linearly independent?

2.Consider the following matrices:
C =
d11 d21 0 0 0 0
d12 d22 0 0 0 0
0 0 c 0 0 0
0 0 0 e11 e12 e13
0 0 0 e21 e22 e23
0 0 0 e31 e32 e33

, D =
d11 d12
d21 d22

, E =
e11 e12 e13
e21 e22 e23
e31 e32 e33

Is it true that det(C) = c ·det(D) ·det(E)?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Linear Algebra

hi Jake204598

welcome to the forum.

Looking at Q1 it looks to me that T is

But what are T2, T3 etc?  I see no definition for these.

Q2. Yes. But showing it from the rules for determinant expansion could get messy.  Have you been given any rules that might make this easier?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob