![]() ![]() It didn't look as neat as the previous solution, but it does show us that there is more than one way to set up and solve matrix equations. In fact it is just like the Inverse we got before, but Transposed (rows and columns swapped over). On the other hand, doing elimination with messy fractions like these cant be a pretty thing. Then (also shown on the Inverse of a Matrix page) the solution is this: Cramers Rule is great, but crunching a bunch of 3 x 3 determinants takes a long time and there are only about 6 billion places to make mistakes. The rows and columns have to be switched over ("transposed"): I want to show you this way, because many people think the solution above is so neat it must be the only way.Īnd because of the way that matrices are multiplied we need to set up the matrices differently now. ![]() Do It Again!įor fun (and to help you learn), let us do this all again, but put matrix "X" first. Quite neat and elegant, and the human does the thinking while the computer does the calculating. We took an adventure on the West Virginia Outlaw Trails up to The View or as the locals call it The Top of The World. Learn vocabulary, terms, and more with flashcards. Just like on the Systems of Linear Equations page. Start studying Unit 1 - Part 1 - Section 1: Visual descriptions of 3x3 Systems of Linear Equations. Then multiply A -1 by B (we can use the Matrix Calculator again): (I left the 1/determinant outside the matrix to make the numbers simpler) It means that we can find the X matrix (the values of x, y and z) by multiplying the inverse of the A matrix by the B matrix.įirst, we need to find the inverse of the A matrix (assuming it exists!) Then (as shown on the Inverse of a Matrix page) the solution is this: ![]() A is the 3x3 matrix of x, y and z coefficients.Which is the first of our original equations above (you might like to check that). Why does go there? Because when we Multiply Matrices we use the "Dot Product" like this: ![]()
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