Hi, I need to solve for a matrix X in the equation below:
What I tried to do was first minus the to the other side, then I took the inverse of and multiplied that on both sides. I thought that taking the inverse and multiplying with it would have a division type of effect. Unfortunately I didn't get the correct answer. Would anyone mind telling me what I've done wrong?
Thanks!
Hmm, throwing it into a matrix calculator online seems to give these values:
-0.263157894736842 -0.315789473684210
-0.473684210526316 -0.368421052631579
Those are consistent with my values, unfortunately after trying to solve the problem with both my own values and your values, I still got the answer wrong in both cases .
I think I must be missing something here *frustration*!
Okay, starting with:
Moving over the second matrix on the left side to the right side:
Should simplify to:
Then I took the inverse of the matrix attached to X and multiplied both sides by it, I'll use the solution that I arrived at for the inverse, though I don't know whether it is right or not at this point:
And my final answer for X came out to be:
If you want me to expand on any of what I've done let me know.
EDIT: Made a correction in my typing up of the math.
i get, as a first step:
i concur with Chris L that the inverse of the first matrix is:
applying this to the RHS after the first step checks out in the original equation. i suggest you double-check your arithmetic, i made several errors verifyng this myself.
one more thing you need to be aware of: matrix multiplcation is NOT commutative.
if AX = B, then X = A^-1B, NOT BA^-1.
the determinant of your original matrix (the one you inverted) is (-7)(5) - (-6)(-9) = -35 - 54 = -89. by a well-known rule, to invert a 2x2 matrix, you swap the upper-left and lower-right corners, and change the sign of the other two entries (leaving them where they are), and then divide each one by the determinant.