Addition and subtraction and multiplying a matrix by a scalar

Matrix Addition and Subtraction

Matrices of the same dimension can be added or subtracted. The resulting matrix will also have the same dimensions as the two initial matrices.
During matrix addition, the elements in the corresponding positions within the two matrices are added together to form the elements of the new matrix.
Similarly, during subtraction, the elements in the corresponding positions within the two matrices are subtracted from each other.
For example, if A = [a1, a2] and B = [b1, b2], then the A + B = [a1+b1, a2+b2] and A - B = [a1-b1, a2-b2].

Any matrix can be multiplied by a scalar (a real number).
When a matrix is multiplied by a scalar, each and every element within the matrix is multiplied by the scalar.
For example, if a matrix A = [a1, a2] is multiplied by a scalar k, then the resulting matrix would be kA = [ka1, ka2].
Scalar multiplication of matrices is both commutative and associative.
Gaining a strong understanding of scalar multiplication and matrix addition is important as it will boost confidence when solving problems related to matrices.

Note that the positions of elements in the matrices are very important in matrix operations.
Always make sure the matrices involved in addition or subtraction have the same dimensions.
To enhance understanding of solving matrix addition, subtraction, and multiplication questions, make use of worked examples and continuously practice previous exercises.
Understand order of operations: scalar multiplication must be performed before addition or subtraction.
It can be useful to use colour or symbols to keep track of which elements correspond to each other when doing these operations.