Final answer:
The student's question refers to the distributive property of transposing a sum of matrices, stated as (A + B + C)^T = A^T + B^T + C^T in the context of linear algebra.
Step-by-step explanation:
The question refers to the distributive property of the transpose operation for matrices, which is a concept in linear algebra within the broader subject of mathematics. When working with matrix transpositions and their properties, an important aspect to understand is that the distributive property of transposition over matrix addition retains parallelism with the principles applied to scalar and vector multiplication.
In general, the distributive property of the transpose operation over matrix addition can be stated as follows:
Let A, B, and C be matrices. Then, the transpose of the sum of A, B, and C is equal to the sum of the transposes of A, B, and C, i.e.,
(A + B + C)T = AT + BT + CT.
This property allows us to individually transpose matrices before summing them, which can be particularly useful in various applications in linear algebra, such as solving systems of equations or working with transformations.
The complete question is: distributive property of transpose for more than two matrix is: