Video Transcript
Given that 𝐴 is equal to one,
zero, five, two, one, zero, zero, two, negative five, 𝐵 is equal to one, negative
two, negative five, negative two, one, two, negative five, negative two, negative
five, where 𝐴 and 𝐵 are both three-by-three matrices, find the transpose of 𝐴
plus 𝐵.
We can start by noting that 𝐴 and
𝐵 are both matrices of the same order, since they’re both three by three. Therefore, we are able to add them
together. So let’s start by doing that. When adding matrices, we simply
take the corresponding elements of each matrix and add them together. Since the first element of 𝐴 is
one and the first element of 𝐵 is also one, the first element of 𝐴 plus 𝐵 will be
one plus one. The second element will be zero
plus negative two. The third element will be five plus
negative five. For the second row, we have two
plus negative two, one plus one, and zero plus two. And for the third row, we have zero
plus negative five, two plus negative two, and negative five plus negative five.
Now, all we need to do is simplify
each of these elements. And we found that 𝐴 plus 𝐵 is
equal to two, negative two, zero, zero, two, two, negative five, zero, negative
10. Now that we have the matrix of 𝐴
plus 𝐵, all we need to do is find the transpose of this matrix to reach our
solution. When finding the transpose of a
matrix, we simply take each of the rows of the original matrix and make them the
columns of the transpose.
So, since the first row of 𝐴 plus
𝐵 is two, negative two, zero, the first column of the transpose of 𝐴 will be two,
negative two, zero. The second row of 𝐴 plus 𝐵 is
zero, two, two. So this will be the second column
of the transpose of 𝐴 plus 𝐵. And our final row in 𝐴 plus 𝐵 is
negative five, zero, negative 10. So this will be the final column of
the transpose of 𝐴 plus 𝐵.
So now we found the transpose of 𝐴
plus 𝐵, giving us a solution of two, zero, negative five, negative two, two, zero,
zero, two, negative 10.
