Find each product, if possible. See Examples 5–7.

Question

Find each product, if possible. See Examples 5–7. <3x2 Matrix><1x3 Matrix>

Accepted Answer

Hello, everyone. We are asked to perform multiplication of the two matrices given below. We are given a two by three matrix where the first row is two negative 73 and the second row is 13. And we're multiplying that by a three by one matrix where the column is negative 259. Our answer choices are a A two by one matrix. 12, 105 is the column B A two by one matrix with a column of 12 negative C A two by one matrix with the column of negative 12, 105 D A one by two matrix where the row is negative 12 105. First thing to recall is that when we multiply matrices, we need to first check the dimensions. Our first matrix is a two by three matrix. And our second matrix is a three by one matrix. The columns of our first matrix must match the rows of our second matrix. In order to multiply in this case, they are both threes. And we can take the rows of the first matrix by the columns of the second matrix to discover the size of our answer. So our answer matrix will be a two by one. So knowing that it's a two by one, I know I'm gonna have two rows and one column. So I find the values within that matrix by first multiplying the corresponding elements of the first row of the first matrix by the first column of the second matrix. So I'm gonna have the first element of the first row multiplied by the first element of the first column. So two multiplied by negative two, we're gonna add that to the first element or sorry. The second element of the first row multiplied by the second element of the first column. So negative seven multiplied by five plus the third element of the first row, three multiplied by the third element of the first column nine. That's our first row in our answer. We won't do it out until I'm done setting it all up next. I'm multiplying the second row in the first matrix by the column in the second matrix. So the first element in the second row is six multiplied by the first element in the column which is negative two, adding that to the second element of the second row which is zero multiplied by the second element of the column which is five and adding to that the third element of the third row or sorry of the second row, which is 13 multiplied by the third element of the column which is nine. Now, I'm gonna do out the multiplication and then we'll do the addition. So we have negative four minus 35 plus 27 as my top row, negative 12 plus zero plus 117 as my second row. Now to find the sum, you gonna combine them and my top row ends up being negative 12. My second row ends up being a positive 105. And that should be our answer matrix. It's a two by one matrix and it has a column that is negative 12 105 and that matches answer choice C have a nice day.

Find each product, if possible. See Examples 5–7. <3x2 Matrix><1x3 Matrix>

Key Concepts

Matrix Multiplication

Dimensions of Matrices

Dot Product

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