Given the matrix 𝐴 which has elements eight, negative three, one, negative two, what is two 𝐴?
In this question, we’re being asked to take the matrix 𝐴 and multiply it by the value two, which is just a scalar. We recall then that, to multiply a matrix by a scalar, we just need to multiply each individual element in our matrix by that scalar. Let’s see what that looks like. Two 𝐴 then will be equal to two multiplied by the matrix with elements eight, negative three, one, negative two.
Multiplying each element of this matrix 𝐴 individually by two will give the matrix with elements two times eight, two times negative three, two times one, and two times negative two. Two times eight is 16. Two times negative three is negative six. Two times one is two. And two times negative two is negative four.
Two 𝐴 then is the two-by-two matrix with elements 16, negative six, two, negative four.