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 for exercise on matrix operations in college algebra course.

Accepted Answer

hey everyone in this problem we are asked to perform the following matrix operation were given negative two A plus five B. Ok. And the matrices were given here. A and B are three by two matrices. You know, we're doing addition subtraction of matrices but we want to first check is that they're the same size? They have the same dimension. So A and B do have the same dimension. So we're okay to go ahead and get started. Okay, So we have negative two A plus five B. And let's just write this out in terms of our matrices. Ok, So this is going to be negative two terms of matrix A. Which has in its first column 764 and in its second column 158. Okay. And then we're adding five times B. Which is the matrix with its first column 418. And second column negative seven negative 90. Okay. Alright. So similarly to if we are adding subtracting and multiplying just with um A and B as variables that aren't matrices. Okay. We want to do that multiplication first. Okay, So we want to deal with the negative two times A and the five times B before we add these two together. Okay, Alright, so negative two. And we have a constant out front of the matrix. What we do is we can bring that constant inside the matrix and it's gonna multiply to every single element. Okay, and so this is going to give us negative two times seven. -2 times 6 -2 times four -2 times one. Negative two times five and negative two times eight. Okay then we're still going to be adding and we're gonna be adding five times B. Okay so same thing we bring that constant of five in and it multiplies to every element. So we have five times 45 times one. Five times eight. Five times negative 75 times negative nine and five times zero. Okay. So just simplifying within each of these matrices we have negative 14 negative 12 negative eight negative two negative 10 negative plus five -35 -45 and zero. Alright. So we figured out essentially what negative to a. Is and what five B is. And now we need to add them together when we're adding matrices together. What we're gonna do is we're gonna add term by term. Okay so each corresponding element is going to be added to the corresponding element in the other matrix. So this is gonna give us negative Plus 20K. So we're taking the element from the first row. First column adding together. Okay then we're gonna move down we're gonna do the same thing 2nd row, first column and add it together. Okay so this one corresponds here and then we're gonna do the same negative 12 plus five. Okay. And that corresponds with those blue values. Alright so now we're gonna keep going with the rest of them. So we get negative 8-plus 40 in the bottom left. We get negative two plus negative 35 in the top rate. We get negative 10 plus negative 45 in the second row and second column. And then we have negative 16 plus zero in the bottom right? Okay. Alright. Simplifying negative 14 plus 20 is gonna give us six negative 12 plus five is going to be negative seven negative eight plus is going to be 32 negative two plus negative 35 negative 37 negative 10 plus negative 45 is negative 55 negative 16 plus zero is negative 16. And so that's our answer. That is negative two plus five. B. Is this matrix here? Okay It's a three by two matrix. The first column has six negative 7 32 and the second column has negative 37 negative 55 negative 16. And that's going to correspond with answer C. That's it for this one. I hope this video helped see you in the next one.

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

Key Concepts

Matrix Addition and Scalar Multiplication

Matrix Dimensions and Compatibility

Order of Operations in Matrix Expressions

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