Consider the matrix 𝐴. Find nine times 𝐴, where 𝐴 is
equal to the one-by-two matrix two, negative one.
In this question, we’re given
matrix 𝐴 and we need to find nine times 𝐴. Remember, nine is just a real
number, so this is scalar multiplication of our matrix. So to answer this question, all we
need to do is recall how we multiply a matrix by a scalar. We do this by multiplying every
single entry inside of our matrix by our scalar. So we need to multiply the entry in
the first row and first column by nine and the entry in the first row and second
column by nine. This gives us the following matrix,
and we can just evaluate this.
In the first row and first column,
we have nine times two, which is of course just equal to 18. And in the first row and second
column, we have nine multiplied by negative one. This is of course just equal to
negative nine, and this gives us our final answer. Therefore, we were able to show if
𝐴 is equal to the one-by-two matrix two, negative one, then nine 𝐴 will be equal
to the one-by-two matrix 18, negative nine.