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The two matrices and their answer must be of the same dimensions.
Each element of the answer matrix is the sum of the elements in the corresponding elements on the matrices that are being added.
In algebraic form,
if A = {aij} where 1 ≤ i ≤ m, 1 ≤ j ≤ n is an mxn matrix
B = {bij} where 1 ≤ i ≤ m, 1 ≤ j ≤ n is an mxn matrix
and C = {cij} = A + B,
then C is an mxn matrix and cij = aij + bij for all 1 ≤ i ≤ m, 1 ≤ j ≤ n
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When adding or subtracting matrices do the dimensions of the sum or differences always match the original matrices?
Yes, because otherwise addition and subtraction are not defined.
Are matrix addition and matrix multiplication commutative?
Matrix addition is commutative if the elements in the matrices are themselves commutative.Matrix multiplication is not commutative.
What makes two matrices equal?
two matrices are normally considered equal only if they are identical. In other words, every element in the matrix must be equal to the corresponding element in the other matrix.
Can the elimnation matrices only be applied to square matrices?
Only square matrices have inverses.
How do you add matrices?
You add matrices by adding their respective terms - e.g. the element in the first row and sixth column of the sum is the sum of the elements in the addends' first rows and sixth columns. Wikipedia has a nice example of matrix addition that I linked below.
