Final answer:
The student's question involves creating an augmented matrix for a given matrix equation and solving that system. Without specific matrices provided, we cannot construct the augmented matrix or provide the solution vector.
Step-by-step explanation:
The student is asking how to write an augmented matrix for the linear system corresponding to a matrix equation and to solve the system represented by that matrix equation. In the context given, assuming a and b are matrices, the matrix equation axb would typically represent a system of linear equations that can be solved using matrix operations. However, since we don't have the actual matrices or their dimensions, we cannot provide the specific augmented matrix or the solution. In order to write the augmented matrix for a system of linear equations, one would typically place the coefficients of the variables in the columns of the matrix and the constants in the last column.
Once the augmented matrix is set up, you can use Gaussian elimination or other matrix operations to solve for the variables. These solutions are then usually represented as a vector of values corresponding to each variable in the system. The requests to use specific equations for vector operations seem to imply operations involving cross products and dot products. Without specific vectors or equations provided, we cannot apply those operations here.