Finding the inverse and finding a matrix * A = 0 matrix

  • Thread starter mr_coffee
  • Start date
  • #1
1,629
1
Hello everyone!! Matrices fun! Anyways,
I'm trying to find a matrix that is equal to the idenity matrix if u multiply 2 matrices together. Well that matrix is the inverse So i'm trying to find the inverse but the answer is wrong:
A =
-5 3
2 -9

So i found the determinant and i switched the a and d, and negated the c and b . isn't htat the inverse?

1/35-6 = 1/29


-9 -3
-2 -5

-9/29 -3/29
-2/29 -5/29

isn't thtat the inverse of A?

I also have B =
-1 6
5 -30

I need to multiply that by some matrix C so the resultant matrix is
0 0
0 0
but i can't just say C is equal to
0 0
0 0
any ideas? thanjks!

I did notice, Row 1 is just 1/5 row 2
 

Answers and Replies

  • #2
TD
Homework Helper
1,022
0
mr_coffee said:
So i found the determinant and i switched the a and d, and negated the c and b . isn't htat the inverse?
You have to switch a and d, also switch b and c and then change the signs of these last 2. After that, you have to divide by the determinant. So:

[tex]A = \left( {\begin{array}{*{20}c}
a & b \\
c & d \\

\end{array} } \right) \Rightarrow A^{ - 1} = \frac{1}
{{\det A}}\operatorname{adj} A = \frac{1}
{{ad - bc}}\left( {\begin{array}{*{20}c}
d & { - c} \\
{ - b} & a \\

\end{array} } \right)[/tex]

mr_coffee said:
I need to multiply that by some matrix C so the resultant matrix is
0 0
0 0
but i can't just say C is equal to
0 0
0 0
any ideas? thanjks!
If you don't "see" it right away, work out the following matrix product to get a system of lineair equations.

[tex]\left( {\begin{array}{*{20}c}
{ - 1} & 6 \\
5 & { - 30} \\

\end{array} } \right) \cdot \left( {\begin{array}{*{20}c}
a & b \\
c & d \\

\end{array} } \right) = \left( {\begin{array}{*{20}c}
0 & 0 \\
0 & 0 \\

\end{array} } \right)[/tex]
 
  • #3
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
19
Multiplying a matrix by something to get zero strongly reminds me of the notion of a null space...
 
  • #4
1,629
1
Thanks TD, but for some reason its still wrong, i got:
-9/29 -2/29
-3/29 -5/29
 
  • #5
TD
Homework Helper
1,022
0
Check your determinant again, that is ad-bc :smile:
 
  • #6
1,629
1
lol what the f, (-5)(-9) - (3)(2)
1/45-6
1/39 right?
 
  • #7
TD
Homework Helper
1,022
0
Well, the determinant is 39 (so not 29). Then, you have to divide by it indeed.
So 1/39 * adj(A)
 

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