Question

Which statement illustrates the Distributive Property of scalar multiplication? (Assume that A and B are matrices and c and d are scalars.) A. A × B = B × A B. c(dA) = cd(A) C. cA − cB = c(A − B) D. cA + dB = cd(A + B)

Answer 1

The correct answer is option C.

cA − cB = c(A − B)

Explanation:

Distributive property of scalar multiplication

It is the product of sum or differences of numbers and with another number.

example

a*(b + c) = ab + ac

a (b - c) = ab - ac

It is given some options,the option C is the example illustrates the Distributive Property of scalar multiplication.

cA − cB = c(A − B)

Answer 2

C.
`cA-cB=c(A-B)`

Explanation:

Given that A and B are matrices and
`c` is a scalar, then the distributive property of scalar multiplication over addition is given by;

`c(A+B)=cA+cB`

The distributive property of scalar multiplication over subtraction is

`c(A-B)=cA-cB`

The correct answer is C.