Video Transcript
If 𝐴 is equal to the one-by-one matrix whose only entry is two, what is three 𝐴?
We’re given a matrix 𝐴, which is a one-by-one matrix with the only entry as two. And we need to find the value of three 𝐴. We can see that three 𝐴 is three multiplied by 𝐴. This is scalar multiplication of a matrix. So to answer this question, we need to recall how we perform scalar multiplication of a matrix.
We recall when we’re performing scalar multiplication of a matrix, we multiply every single entry inside of our matrix by our scalar. In this case, we’re going to need to multiply every single entry by three. So three 𝐴 is equal to three multiplied by the one-by-one matrix whose only entry is two. And then to perform this scalar multiplication, we need to multiply every single entry inside of our matrix by our scalar, in this case three.
However, this is only a one-by-one matrix. So it only has one entry, which is two, giving us the one-by-one matrix whose entry is three times two. And of course, three times two is equal to six. So this gives us our final answer, which is the one-by-one matrix whose only entry is six. Therefore, by multiplying every single entry inside of our matrix by our scalar three, we were able to show if 𝐴 is equal to the one-by-one matrix whose only entry is two, then three 𝐴 is equal to the one-by-one matrix whose only entry is six.
