Question

Without calculating determinant of matrix A, B, and C, how can I find whether [A]+[B] = [C]?

Answer 1

Matrix A and matrix B must have the same dimension in order for their addition to be defined.

Answer 2

if they have the same dimension, what should I do next?

Answer 3

Is a specific dimension given?

Answer 4

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.

Answer 5

@mathteacher1729

A=\[\left[\begin{matrix}1&2&4&0 \\1 &1&7&2\\4&2&-3&1\\5&9&2&8\end{matrix}\right]\]

B=\[\left[\begin{matrix}1&2&4&0\\0&-1&3&2\\2&1&1&-1\\3&8&1&9\end{matrix}\right]\]

C=\[\left[\begin{matrix}1&2&4 & 0\\0& -1&3&2\\6&3&-2&0\\5&9&2&8\end{matrix}\right]\]

Answer 6

This does not appear to be a determinant problem at all. Simply add the matrices and see if A + B = C ?

Answer 7

nah,they're not the same but I still have to prove that [A]+[B}=[C]

Answer 8

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 ?

Answer 9

yes

Answer 10

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)

http://tutorial.math.lamar.edu/Classes/LinAlg/DeterminantByRowReduction.aspx

Answer 11

okay, thank you!