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). Then (also shown on the Inverse of a Matrix page) the solution is this: 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. Just like on the Systems of Linear Equations page. 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.Instead of multiplying one equation in order to eliminate a variable when the equations were added, you could have. Which is the first of our original equations above (you might like to check that). There are other ways to solve this system. Why does go there? Because when we Multiply Matrices we use the "Dot Product" like this:
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