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Video: Finding the Difference between Two Given Matrices

Chris O’Reilly

Find the matrix 7, 9, −5, 0 − the matrix 8, −5, 2, 0.

02:16

Video Transcript

Find the matrix seven, nine, negative five, zero minus the matrix eight, negative five, two, zero.

Before we do the subtraction and subtract one matrix from the other, we need to remember a quick tip. And that tip or that reminder is that you can only add or subtract matrices that actually have the same dimensions. Well, if we actually look back at the question, we can see that actually both the matrices are two by two. So therefore, they are equal. And we actually can do the subtraction.

So when we actually subtract matrices, what we’re going to be doing is subtracting the corresponding elements. So first of all, we’re actually gonna have seven minus eight, as that’s a seven in the first matrix minus eight is a corresponding element in the second matrix. And then we’re gonna have nine minus negative five.

Again, we have the nine from the first matrix. And the corresponding element in our second matrix is negative five. Then we have negative five minus two. Again, these are our corresponding elements. And then finally we get zero minus zero.

So, great! We’re at the point now where all we need to do is we actually calculate each of our elements for our final matrix. So our first element will be negative one because it’s seven minus eight. Our first element is going to be negative one because it’s seven minus eight, our next element being 14 because we have nine minus negative five.

Be careful of negatives because what we have here is nine minus negative, which means the same as plus, so the same as nine plus five, which is 14. And then our next element is negative seven because it’s negative five minus two. And then finally our last element is zero because it’s zero minus zero.

So therefore, we can say that if we have the matrix seven, nine, negative five, zero and then we subtract the matrix eight, negative five, two, zero, we arrive at the matrix of negative one, 14, negative seven, zero.