Today was one of the longer days we've had in a while. First, we solved equations that involved adding and subtracting to solve for the missing variable. This was easy - just add or subtract the matrix on both sides to get the answer. Note that your answer represents an ENTIRE matrix, not just a number.
Equations involving multiplication were trickier. We know the opposite of multiplication is divison. However, we cannot divide matrices. So, as an alternative, we need to:
1. Find the inverse of the matrix next to the variable. To do this, recall that you must find the determinant, then multiply every element in the matrix by 1/determinant.
2. Once you find the inverse, multiply both sides of the equation by the inverse. The two matrices on the side with the variable cross each other out because they are the inverse of each other. It doesn't matter that they don't contain the same numbers - they're still inverses, so they still cross out. Bring the variable down.
Then, multiply the two matrices on the other side. Remember, you must multiply the first row with the first column, then first row with the second column, then the second row with the second column, then the second row with the second column. The resulting matrix will be your answer.
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