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 here we are asked to perform the following matrix operation negative two times A plus four times B. Now the first step here in solving we just want to substitute in the given matrices in to the corresponding variables. So first we have negative two times matrix A which is given as a three by one matrix the values five negative six and two. We then have plus times matrix B which is also given as a three by one. Matrix with the values negative +70 and negative three. And next we just want to take each scalar value and multiply them by each value in the matrix. So with our first matrix here, matrix A we take negative two and multiply it by each input. So beginning with our first value we have negative two times five. We then have negative two times negative six. And lastly we have negative two times two. And now we have plus the second matrix which each input will be multiplied by the scalar four. So beginning again with the first value we have four times negative seven. We then have four times zero. And lastly we have four times negative three. And now the next step we just want to simplify both matrices. So again beginning with this first matrix here we have negative two times five giving us negative 10, then negative two times negative six, giving us positive 12. And lastly negative two times two giving us negative four. And now moving on to the second matrix we have four times negative seven which is negative 28 4 times zero is just zero and four times negative three gives us negative 12. And now we are just left with adding these matrices together. So we just have to add each corresponding term to the other matrix. And so what I mean here is we start with our first term in matrix A. Or what was matrix A. And we take negative 10 and then added to the first term in matrix B. So plus negative 28. We then have the next term. So we have 12 plus zero and lastly negative four plus negative 12. And now the last step here is to simply add these terms together and simplify the matrix. So we're left with negative two A plus four B. Being the three by one. Matrix with the values of negative 10 plus negative 28 which gives us negative 38. Then 12 plus zero is simply 12. And lastly negative four plus negative 12 gives us negative 16. And this leaves us with answer choice. D Thanks for watching. I hope you found this video helpful and I'll see you again next time

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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