Video: Multiplying a Matrix by a Scalar

Consider the matrix 𝐴. Find 9𝐴. 𝐴 = [2, βˆ’1].

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Video Transcript

Consider the matrix 𝐴. Find nine times 𝐴, where 𝐴 is equal to the one-by-two matrix two, negative one.

In this question, we’re given matrix 𝐴 and we need to find nine times 𝐴. Remember, nine is just a real number, so this is scalar multiplication of our matrix. So to answer this question, all we need to do is recall how we multiply a matrix by a scalar. We do this by multiplying every single entry inside of our matrix by our scalar. So we need to multiply the entry in the first row and first column by nine and the entry in the first row and second column by nine. This gives us the following matrix, and we can just evaluate this.

In the first row and first column, we have nine times two, which is of course just equal to 18. And in the first row and second column, we have nine multiplied by negative one. This is of course just equal to negative nine, and this gives us our final answer. Therefore, we were able to show if 𝐴 is equal to the one-by-two matrix two, negative one, then nine 𝐴 will be equal to the one-by-two matrix 18, negative nine.

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