Matrices Addition, subtraction, and scalar operations

Addition and subtraction Addition and subtraction of matrices can only be performed if the matrices are of the same order. Addition and subtraction of matrices is performed by adding or subtracting the corresponding elements. Example, Ex 16B, Q.1

Scalar multiplication When a matrix is multiplied by a scalar, each element of the matrix is multiplied by the scalar. The order of the matrix is unchanged. Example, Ex 16B, Q.5

You do Ex 16B, Q. 2, 3, 6

Properties of addition of matrices: PropertyExample Commutative (doesn’t matter which order) A + B = B + A Associative (doesn’t matter where the brackets are) (A + B) + C = A + (B + C) (kc)A = k(cA) IdentityA + O = O + A InverseA + A = O = A + A DistributivekA + kB = k(A + B) kA + cA = (k + c)A

Simple matrix equations Simple matrix equations that require the addition or subtraction of a matrix or multiplication of a scalar can be solved in a similar way to algebraic equations. Example, Ex 16B, Q.7, 9

You do Ex 16B, Q. 10, 12, 13, 14