(A+B)+C and that (A+B=A+B 2.4 Matrix Multiplication Matrices are multiplied by using the inner product. The inner product of two vectors. a and b, is a scalar and is written a'b=anb+a2b2 +.+anbn= ba For an n x k matrix A and a k x T matrix B, the product matrix C= AB is an n x T matrix whose ith element is the inner product of row i of A and column k of B. generally, AB+BA The product of a matrix and a vector is a vector and is written as C= Ab ba1+ b2a+.+ bak where 6, are ith element of vector b and a are ith column of matrix A. here we see that the right-hand side is a linear combination of the columns of the matrix where the coefficients are the elements of the vector In the calculation of a matrix product C= Anxk BkxT, it can be written as aB where b: are ith column of matrix B Some general rules for matrix multiplication are as follow Associate law:(ABC=A(BC) Distributive law: A(B+C)=AB+AC Transpose of a product:(AB)=BA Scalar multiplication: aa=[aaik]fo(A + B) + C = A + (B + C), and that (A + B) ′ = A′ + B′ . 2.4 Matrix Multiplication Matrices are multiplied by using the inner product. The inner product of two vectors, an and bn, is a scalar and is written a ′b = a1b1 + a2b2 + ... + anbn = b ′a. For an n × k matrix A and a k × T matrix B, the product matrix, C = AB, is an n × T matrix whose ikth element is the inner product of row i of A and column k of B. Generally, AB 6= BA. The product of a matrix and a vector is a vector and is written as c = Ab = b1a1 + b2a2 + ... + bkak, where bi are ith element of vector b and ai are ith column of matrix A. Here we see that the right-hand side is a linear combination of the columns of the matrix where the coefficients are the elements of the vector. In the calculation of a matrix product C = An×kBk×T , it can be written as C = AB = [Ab1 Ab2 AbT], where bi are ith column of matrix B. Some general rules for matrix multiplication are as follow: Associate law: (AB)C = A(BC). Distributive law: A(B + C) = AB + AC. Transpose of a product: (AB) ′ = B′A′ . Scalar multiplication: αA = [αaik] for a scalar α. 3