Video: Addition of Two-by-Two Matrices

Evaluate [8, 11 and −3, 7] + [10, −1 and 3, 1].

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Video Transcript

Evaluate the matrix eight, 11, negative three, seven plus the matrix 10, negative one, three, one.

So, when we add matrices together, what we do is we add the corresponding elements and then create a new matrix. It’s worth noting that you can only add matrices if they have the same dimensions. So, in our case, both the matrices that we’re looking at are two-by-two. So, that means that we can add them. It also means that our result is gonna be a two-by-two matrix.

So, if we take a look at our matrices, the first thing we’re gonna do is we’re gonna add the first element, which is the first element in both of our matrices, the top-left element. So, if we add eight and 10, what we’re gonna get is 18. Then, we move across to the second element in the first row. And we’re gonna have 11 add negative one. Well, it is the same as 11 minus one, which gives us 10.

So, then, we have our bottom-left element, which is negative three add three, which is just gonna give us zero. And then, our final element is gonna be seven add one, which gives us eight. So, we can say that our final matrix is 18, 10, zero, eight. And this is the result of the matrix eight, 11, negative three, seven and the matrix 10, negative one, three, one.

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