Math  /  Algebra

QuestionGiven the matrices AA and BB shown below, find A+BA+B. A=[545]B=[403]A=\left[\begin{array}{c} -5 \\ 4 \\ 5 \end{array}\right] \quad B=\left[\begin{array}{c} -4 \\ 0 \\ -3 \end{array}\right]

Studdy Solution

STEP 1

What is this asking? We're adding two matrices, which are just like fancy lists of numbers! Watch out! Matrices can only be added if they have the same dimensions.
These both have 3 rows and 1 column, so we're good to go!

STEP 2

1. Add the corresponding entries

STEP 3

Alright, let's **add** the numbers in the same positions in each matrix.
Think of it like this: the top-left corners get added together, the top-right corners get added together, and so on.
Here, we only have one column, so we'll add the top entries, the middle entries, and then the bottom entries.
This is how we add matrices!

STEP 4

Let's do the top entries first.
We have 5-5 from matrix AA and 4-4 from matrix BB.
Adding them together, we get 5+(4)=9-5 + (-4) = -9.
So, the top entry of our new matrix is going to be 9\mathbf{-9}!

STEP 5

Now for the middle entries!
We have 44 from AA and 00 from BB.
Adding them gives us 4+0=44 + 0 = 4.
The middle entry of our new matrix is 4\mathbf{4}!

STEP 6

Finally, the bottom entries!
We have 55 from AA and 3-3 from BB.
Adding them gives us 5+(3)=25 + (-3) = 2.
The bottom entry of our new matrix is 2\mathbf{2}!

STEP 7

Putting it all together, our new matrix, A+BA + B, is: (942)\begin{pmatrix} -9 \\ 4 \\ 2 \end{pmatrix}

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