Matrices: Transpose and Inverse

  • Thread starter PotentialE
  • Start date
  • #1
57
0

Homework Statement


Find (X * Y-1)T - (Y * X-1)T
When X = [3 5]
..............[1 2]
and Y = [3 4]
...........[2 3]

Homework Equations


Inverse= 1/ad-bc [d -b]
........................[-c a]

The Attempt at a Solution


I got:
[9 -6 ]
[14 -9]

But the answer is:
[-3 -2]
[6 3]


I did the problem twice and got the same answer so I don't think its a simple math error, any insight as to how to solve this correctly / what I've done wrong?
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
36,163
6,781
It's rather hard to say where you've gone wrong without seeing your working. Your equations are correct.
 
  • #3
57
0
Well first I did the inverse of Y and got:
[3 -4]
[-2 3]

Then I multiplied that by X and got:
[5 7]
[-3 -4]

Then I transposed it and got:
[5 -3]
[7 -4]

Then I did the inverse of X and got:
[2 -5]
[-1 3]

Multiplied by Y and got:
[-4 -7]
[3 5]

Then I transposed that and got:
[-4 3]
[-7 5]

Then I subtracted the two transposed matrices to get:
[9 -6]
[14 -9]

Seems coherent to me but it's very far from the right answer
 
  • #4
hotvette
Homework Helper
996
5
In your second step, looks like you did Y-1*X instead of X*Y-1
 
  • #5
57
0
Oh that's right!!! I forgot the associative property is non-applicable to matrices. THanks for your help.
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
36,163
6,781
I forgot the associative property is non-applicable to matrices.
No, matrices are associative, A(BC) = (A B)C, but they are not always commutative.
 

Related Threads on Matrices: Transpose and Inverse

Replies
2
Views
3K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
9
Views
5K
Replies
8
Views
2K
  • Last Post
Replies
4
Views
8K
  • Last Post
Replies
2
Views
2K
Replies
3
Views
3K
Top