Consider the matrix 𝐴 equals the matrix negative one, negative one, five, 13, negative one, zero. Suppose the sum of the matrices 𝐴 and 𝐵 is 𝐴 plus 𝐵 is equal to the matrix one, zero, negative one, zero, one, two. Find the matrix 𝐵.
Well, if we’re looking for matrix 𝐵, we can say that 𝐵 is equal to 𝐴 plus 𝐵 minus 𝐴. And this is because if we have 𝐴 minus 𝐴, so this leaves us with zero. So it’d just be 𝐵 is equal to 𝐵. So that give us our matrix 𝐵. So what we’re gonna have is 𝐵 is equal to. Then we’ve got the matrix one, zero, negative one, zero, one, two. That represents 𝐴 plus 𝐵. And then this is minus our matrix 𝐴, which is negative one, negative one, five, 13, negative one, zero.
Now to calculate this, what we do is we subtract the corresponding elements. So therefore, if we look at the first element, we’d have one minus negative one. Well, if you subtract a negative, it’s the same as adding. So it’ll be one plus one. So our first element will be two. And then our next element is zero minus negative one, which will be zero plus one, which gives us one. Then we have negative one minus five, which gives us negative six.
Then our first element on the bottom row is gonna be zero minus 13, which will give us negative 13. Then one minus negative one, which gives us two. And then, finally, two minus zero, which is just two. So we’ve now got matrix 𝐵. And that is the matrix two, one, negative six, negative 13, two, two.
And as we said, we got that by subtracting the matrix 𝐴, which is negative one, negative one, five, 13, negative one, zero away from the matrix formed when we added 𝐴 and 𝐵, which was the matrix one, zero, negative one, zero, one, two.