matrix multiplication tutor

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., (i) A(B +..

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 ..

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..

Multiplication of Matrices - 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..

(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 (Dis..

A matrix of order m x n whose elements are all 0 is called a null matrix (or zero matrix) of order m x n. It is usually denoted by O or more clearly [O] m , n..

Solve the system of equations by using the multiplicative inverse of a matrix. x + z = 4 y + z = 3 x + y = 1 => (4, 0, 0) or (3, 2, 1) or (1, 0, 3) or (2, 0, 2)..

Use augmented matrices to find the multiplicative inverse of the matrix B = ( 5 10 2 4 ) . => ( 1 0 0 1 ) or ( - 5 - 10 - 2 - 4 ) or ( 4 - 10 - 2 5 ) or does not exist..