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I need to find the pair of matrices that are inverses, but I don't fully understand how to inverse matrices.
P = [3 1_-4 0] q = [4 4_12 21]
R = [0 -1/4_1 3/4]
S = [7/12 -1/9_-1/3 1/9]
T = [4 -5 2_8 -1 3]
U = [-9 6 4_-5 -2 3]
V = [3 1_0 2_-4 5]
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answer choices:
a. S and R
b. Q and R
c. P and Q
d. Q and S
if you could explain it to me that would be great, thanks.
You can either,
Multiply the four choices a,b,c,d out.
or find each of there determinants.
If B is the inverse of A then AB= I
So the answer will be what two matrix multiply together to give the identity matrix.
Finding their determinants you say B is the inverse of A and Det(A) = 2, then Det(A-1)=Det(B)=1/2
This means Det(A)Det(B)=1 which means A and B are inverses.
I'd probably multiply them all out its good practice
I'm also dealing with fractions, which is the main part of the confusion I am having with inversesQuote:
Originally Posted by Daniiel
Oh okay, with fractions the calculation is a little bit more annoying, but exactly the same process.
For example a)
S = [7/12 -1/9_]
R = [0 -1/4_1 3/4]
SR =
7/12 -1/9 ) ( 0 -1/4
-1/3 1/9 ) ( 1 3/4
=
-1/9 (7/12)(-1/4) +(-1/9)(3/4) (can already tell its not I since top r ow isn't 1 0
1/9 (-1/3)(-1/4) + (-1/3)(3/4)
So S and R are not inverse,
alternatively
Det(S) = 1/36 and Det(R) = -1/4 showing that they are not inverses
If your still having trouble with fractions one thing you can do is take out factors,
so R = [0 -1/4_1 3/4] = 1/4 * [0 -1_4 3]
Then you simply multiply in the fraction after multiplying the matrix to another