Find each product, if possible.

Question

[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 7 \end{matrix}]

Accepted Answer

Hello, everyone. We are asked to perform multiplication on the two matrices given below. We are given a two by two matrix with the first row as 57. And the second row is 6 11 and a two by one matrix where the column is negative 25, our answer choices are a, a two by one matrix with the column negative 25 B A two by one matrix with the column 25 C A one by two matrix where the row is 25 D A two by one matrix where the column is 43. Recall that the first thing when we want to multiply matrices is we want to look at their dimensions. We are given a two by two matrix and a two by one matrix. In order to multiply them, the columns of the first matrix must match the rows of the second matrix. And in this case, they do. And the rows of the first matrix by the columns of the second matrix tell us the size of our answer. So our solution matrix will be a two by one. So we're gonna have two rows and one column to find the values in our solution matrix. We first are gonna multiply together the first row of the first matrix by the first column of the second matrix. And we multiply the corresponding locations meaning the first element of the first row five gets multiplied by the first element of the first column negative two. And we add that to the product of the second element of the first row, multiplied by the second element of the first column. Next, I'm gonna do the same with the second row from my two by two matrix. So the first element of the second row is six that will be multiplied by the first element of the column which is negative two. And we're gonna add to that the product of the second element of the second row, which is 11 multiplied by the second element of the column which is five. Now I'm gonna do out the products and I get negative plus 35 is my first element negative 12 plus 55 is my second element adding those together. I get 25 as my first element and 43 as my second element. So it looks like my solution here is the two by one matrix 25 43. And that's answer choice D have a nice day.

Find each product, if possible.
$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 7 \end{matrix}]$

Key Concepts

Matrix Multiplication

Matrix Dimensions and Compatibility

1x2 Matrix Structure

Watch next