the properties of scalar multiplication

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 ..

Multiplication of Vectors by Real Numbers, i.e., Scalar Multiple of a Vector - The multiplication of a vector by a real number assumes a lot of significance in such statements as - velocity of car B is double the velocity of car A l . When a vector is multipl..

(c f) (x) = c.f (x) for all x Domain (..

The multiplication of a vector by a real number assumes a lot of significance in such statements as - velocity of car B is double the velocity of car A l..

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 + C) = AB + BC (ii) (A + B)C = AB + AC wh..

Which represents the distributive property of multiplication? => a ( b + c ) = a b + a c or a + b = b + a or ( ab ) c = a ( bc ) or a (1) = a..

Which statement illustrates the associative property of multiplication? => (3 x ) y = y (3 x ) or (3 x ) y = ( x · 3) y or (3 x ) y = 3 x y or (3 x ) y = 3( x y )..

Which of the following satisfies the identity property of multiplication? => 1 × 1 = 1 or 1 - 1 = 0 or 1 + 1 = 2 or 1 × 0 = 0..

Which of the following illustrates multiplicative property of zero? => 23 × 0 = 0 or 57 + 0 = 57 or 18 × 5 = 5 × 18 or 52 + 41.6 = 41.6 + 52..