definition 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 . When a vector is multiplied by a real number, say l , then we get another vector l . The magnitude of l is l times the magnitude of ...

A scalar matrix is a diagonal matrix in which all the diagonal elements are equa..

Kinematics..

Dot Product of Vectors and the Resolution of a Vector - It was mentioned earlier that, displacement vectors are added to displacement vectors, or velocity vectors are added to velocity vectors. Just as it is meaningless to add scalar quantities of different kinds, such as mass and tempera..

Equality of Matrices, Addition of Matrices, Matrix Addition is commutative, Matrix addition is associative, Subtraction of Matrices, Multiplication of a matrix by a scalar, Multiplication of Matrices, Properties of Matrix Multiplication, Transpose of a ..

The following are the Operation on Real Functions: Sum Function, Difference Function, Product Function, Quotient Function, Scalar Multiplication Function, Composite Functions, Inverse Function..