anonymous
  • anonymous
Without calculating determinant of matrix A, B, and C, how can I find whether [A]+[B] = [C]?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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mathteacher1729
  • mathteacher1729
Matrix A and matrix B must have the same dimension in order for their addition to be defined.
anonymous
  • anonymous
if they have the same dimension, what should I do next?
mathteacher1729
  • mathteacher1729
Is a specific dimension given?

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anonymous
  • anonymous
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.
anonymous
  • anonymous
@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=\[\left[\begin{matrix}1&2&4 & 0\\0& -1&3&2\\6&3&-2&0\\5&9&2&8\end{matrix}\right]\]
mathteacher1729
  • mathteacher1729
This does not appear to be a determinant problem at all. Simply add the matrices and see if A + B = C ?
anonymous
  • anonymous
nah,they're not the same but I still have to prove that [A]+[B}=[C]
mathteacher1729
  • mathteacher1729
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 ?
anonymous
  • anonymous
yes
mathteacher1729
  • mathteacher1729
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
anonymous
  • anonymous
okay, thank you!

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