matrix multiplication is distributive

Matrix multiplication is not commutative in general. Matrix multiplication is associative i.e., (AB)C = A(BC), whenever both sides are defined. Matrix multiplication is distributive over matrix addition i.e., ..

When a matrix is multiplied by a scalar factor k, then each element of the matrix is multiplied by ..

Let A=[a i j ] be an m x n matrix and k be any number called a scalar. Then the matrix obtained by multiplying every element of A by k is called the scalar multiple of A by k and is denoted by kA. Thus, kA = [k a i j ] m x ..

When a matrix is multiplied by a scalar factor k, then each element of the matrix is multiplied by ..

(1) A x I = I x A = A where I denotes a unit matrix of suitable order. Matrix I possesses identity property of multiplication, I is called a unit matrix or identity matrix. (2) , it does not have commutative property. (3) A(B + C) = AB + AC (..

Two matrices A and B can be multiplied if the number of columns of A is equal to the number of rows of B. The resultant matrix will be of the order of (number of rows of A x number of columns of B). If A be a matrix of the order m x n and B be a matrix of t..

Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix..

Let us consider the sales done by a school canteen for two successive days. Monday 25 cokes 12 cakes Tuesday 40 cokes 7 cakes Each coke costs $ 5 and cake costs $ 10. The sales can be expressed as a 2 x 2 matrix and the price as a 2 x 1 matrix as given below: The amount collecte..

Fibrocytes are stellate or star shaped cells, which produce the matrix and white and yellow fibres. Macrophages are irregular, amoeboid cells which can ingest bacteria and other disease producing germs by phagocytosis. Mast cells are spherical or oval cells, which produce the anti..

Hund's Rule of Maximum Multiplicity - According to this rule, electron pairing will not take place in orbitals of same energy (same sub-shell) until each orbital is first singly filled with parallel spin. In other words in a set of orbitals having same energy (degenerate orbitals), the el..