In Exercises 9 - 16, find the following matrices: d. - 3A + 2B...

Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Matrices A and B with values A = [6 2 -3], B = [4 -2 3] for matrix operations.

Accepted Answer

hey everyone in this problem. We are asked to perform the following matrix operation. We have negative A plus four B. Okay. And the matrices were given our A is equal to 56 negative seven and B is equal to eight negative 9. 10. Okay, so they're won by three matrices. Alright. To writing out what we want negative A plus four B. And reading this in terms of matrices we have negative 56 negative seven K. Plus four times B. Which is eight negative nine and 10. All right. So before we do the addition, we want to do the multiplication of the constants K. Similar to when we multiply and add normally we do the multiplication first. We're gonna do the same thing here. Okay, when we're doing taking a matrix and multiplying it by a constant. It's just gonna be element wise multiplication. Okay, so that constant is gonna come inside the matrix and it's going to multiply every single element. So applying this to the first we have negative one times this matrix A. Ok, We're gonna bring that negative one inside. We're gonna get negative five negative six. And negative negative seven. And then we're gonna add. Okay, and the second thing we have four times B. And again that constant bar is going to come inside and be and multiply every single. Okay, so we're going to get four times eight. four times negative nine And four times 10. Alright, simplifying here, We get 5 -6. plus four times 8 32. Four times 9 -36 and four times 1040. All right now we just have two matrices we want to add them together. Okay first we need to check that they are the same dimension. Okay, these are both one by three matrices so they're the same dimensions. So we're okay to add them. Okay, But always double check when you're adding that. The matrices have the same dimension and when we add this is also an element wise operation. Okay, so we're going to take an element in A and we're going to add it to the corresponding element and be okay we're going to do that for all of the elements. So let's see this in action. So we're gonna take the first element in a negative five. We're going to add it to the first element in B And sorry, this is negative A. And four B. Okay, so the first element in the first matrix. The first element in the second matrix. And we're gonna add them together and that's gonna be the first element in our resulting matrix. So we have negative five plus 32. Okay, coming from those two red terms, We're gonna do the same thing for the second. Okay, so first row. 2nd column in the first matrix we have negative six. The second matrix we have negative 36. And so we're going to get negative six plus negative 36 in that first row second column of our resulting matrix. Okay. And same thing for the final term. We get seven plus 40. Mhm. Alright so now we have this down to one matrix like we want we just need to simplify each of these terms. So negative five plus 32. That's going to give us 27 negative six plus negative 36 is gonna give us negative 42 7 plus 40 is gonna give us 47. Okay. And so the result negative A. Plus four B. Is going to be the matrix with one row three columns and it's gonna be 27 negative 42 47 that's gonna correspond with answer be that's it for this one. Thanks everyone for watching. I hope this video helped.

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Key Concepts

Matrix Scalar Multiplication

Matrix Addition and Subtraction

Matrix Representation and Notation

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