Matrix A( Matrix B+Matrix C)=?

Question

Matrix A= 7  -7          Matrix B=3   0   -1          Matrix C=x   1   w

               0   8                         2   -1   1                        z   r    4

               0  -8

 

I need to know what the sum/product of this equation is: A(B+C)=?

Answer 1

Matrix addition is pretty straightforward where you add each element in the same location. So if [A]+[B]=[C], then [A]₁₁+[B]₁₁=[C]₁₁ and [A]₂₁+[B]₂₁=[C]₂₁, which can be seen in more detail in the link below

http://www.mathcentre.ac.uk/resources/uploaded/sigma-matrices3-2009-1.pdf

 

Multiplying matrices is a little more complicated but not too bad. Just remember row times column. Where the first element from a row and the first element from are column are multiplied, which is then added to the second elements from the row/column and so on until the end of the matrix is reached (the first matrix must have as many columns as the second has rows so it ends evenly for both). This addition of these multiplications gives the first element of the final matrix (C₁₁). Starting a row lower in the first matrix gives (C₂₁), and starting one row lower gives (C₃₁). While starting one column to the right gives (C₁₂) and so on. this can be seen in the link below

http://www.mathsisfun.com/algebra/matrix-multiplying.html

 

I'll just note the size of the matrix during multiplication is always in the form

[A]_u*v*[B]_v*w=[C]_u*w 

Where the inner sizes have to match (v in this example) and the outer sizes are the final matrix size (u and w). Remember that its [Matrix]_Rows*Columns