In Exercises 9 - 16, find the following matrices: c. - 4A

Question

Matrices A and B for exercise 15 in college algebra, chapter on matrices and determinants.

Accepted Answer

Hey everyone in this problem we are asked to perform the following matrix operation nine A. Okay. And the matrix A. Is a three by three matrix with first row three negative two negative three. Second row 7 to 2 and third row five negative one and zero. Okay so writing out what we want, we want to find Nine A. Okay. And let's just write this in terms of our matrix we have nine times the matrix A 375. In the first column negative 22 negative one. In the second column negative 3 to 0. In the third call. Now when we're multiplying a matrix by a constant we can take that constant into the matrix and multiply it to every single element. Okay this is an element wise operation so we can multiply that constant. Every single element who were gonna end up with is the matrix we have nine times the first element three. Nine times the second element. Seven and same thing for each element. So we get nine times five. In the second column we have nine times negative two, nine times two and nine times negative one. And in the final column nine times negative 39 times two and nine times zero. We're multiplying every element by our constant nine. And now we have just simple multiplication within this matrix to do so nine times three normal multiplication 9 times 7 63. 9 times 5 45. Okay. In the second column we get negative 18, 18 negative nine negative 27 18 and zero. Okay. And so this is the resulting matrix, nine A Hey, it's a three by three matrix with first row, 27 negative 18 negative 27 2nd row 63 18, 18 and third row 45 negative nine and zero. And that's going to correspond with answer A Okay, 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: c. - 4A

Key Concepts

Matrix Scalar Multiplication

Matrix Notation and Dimensions

Matrix Operations in Algebra

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