Final answer:
The equation provided has a dimensional mismatch that makes it unsolvable in its current form. If the matrices were correctly dimensioned as 2x2 rather than 2x4, one could perform matrix multiplication, add the resultant vector to the given vector, and solve the resulting system of linear equations to find x1 and x2.
Step-by-step explanation:
To solve the equation given as:
[3 2 5 5] [x1 x2] + [1 2] = [2 -3]
We first need to understand this expression. The notation suggests we're dealing with matrix multiplication and addition. The expression can be seen as the multiplication of a 2x4 matrix (left side) with a 2x1 vector (middle) to which another 2x1 vector (right side) is added, equaling a 2x1 vector (right-most side).
However, a 2x4 matrix cannot be multiplied by a 2x1 vector, which indicates there might be a typo in the question. Ideally, the 2x4 matrix should be a 2x2 to match the dimensions for multiplication with a 2x1 vector. So first, please check the dimensions of the matrices provided in your question for accuracy. If they are indeed supposed to be 2x2 matrices, you could follow these steps:
- Perform the matrix multiplication between the 2x2 matrix and the 2x1 vector.
- Add the resulting 2x1 vector from step one with the additional 2x1 vector provided in the question.
- Equal the result with the given 2x1 vector on the other side of the equation.
- Solve the resulting system of linear equations for x1 and x2.
Without the correct matrix dimensions, we cannot proceed with the solution. If corrected to a 2x2 matrix, you could use methods like substitution, elimination, or matrix inversion (if applicable) to find the values of x1 and x2.