Without calculating determinant of matrix A, B, and C, how can I find whether [A]+[B] = [C]?
Stacey Warren - Expert brainly.com
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Matrix A and matrix B must have the same dimension in order for their addition to be defined.
if they have the same dimension, what should I do next?
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well u don't need to find the determinant of any matrix.
u just add the corresponding elements of matrix A and matrix B and see whether u get matrix C or not. so the question of finding the determinant does not arise.
This does not appear to be a determinant problem at all. Simply add the matrices and see if A + B = C ?
nah,they're not the same but I still have to prove that [A]+[B}=[C]
I'm sorry but the problem statement is not clear. do you mean:
Det(A) + Det(B) = Det(C) ? where Det(X) means The determinant of matrix X ?
You need to pay careful attention to the elementary row operations you are performing on each matrix. (Thm 1 from this link sums it up nicely)