Final answer:
The student is seeking to construct a 2x3 matrix C with entries of 1s and 0s such that the product AC gives a specific result. The process would involve trial and error, placing 1s and 0s in C to satisfy the multiplication with a given A matrix.
Step-by-step explanation:
The question appears to be asking for the construction of a 2x3 matrix C using only the numbers 1 and 0, such that when C is multiplied by another matrix A, the resulting product is matrix AC. To find such a matrix C, one would typically use trial and error, experimenting with different combinations of 1s and 0s in the matrix until the desired result is achieved. For example, if the matrix A is known, we can place 1s in positions of matrix C that would give a result of 1 when using matrix multiplication rules, and 0s elsewhere. The question has also mentioned orthogonality, which might imply that matrices A and C are orthogonal, but without additional information, this is difficult to address.