Perform each operation, if possible.

Question

[\begin{matrix} - 1 & 0 \\ 2 & 5 \end{matrix}] [\begin{matrix} - 3 & 4 \\ 2 & 8 \end{matrix}]

Accepted Answer

Hello, everyone. We are asked to apply the given operations on the following matrices. We are given 22 by two matrices. The first row of the first matrix reads negative 20. The second row is 47. The second matrix, the first row is negative 87. The second row is 9 13. We are given four answer choices all of which are two by two matrices. Knowing that both of our original matrices are two by two. We can ensure this can be multiplied because the columns from the first matrix match the rows from the second matrix. And we can say that our answer matrix will be a two by two based on the dimensions of the original matrices. So to find the elements of our new matrix for the first element of the first row, we are going to multiply the first row of the first matrix by the first column of the second matrix. So we will have the first element of the first row is negative two. We are going to multiply that by the first element of the first column of the second matrix which is negative eight, we are gonna add the product of the second element of the first row from the first matrix which is zero multiplied by the second element of the first column of the second matrix which is nine. Now, for the next element, we're going to go to the right. And this will be the first row of the first matrix and the second column of the second matrix. So we have negative two multiplied by seven as the first element of the second column plus zero multiplied by 13 as 13 is the second element of that second column going to the second row of our solution matrix, we are gonna use the second row of the first matrix and the first column of the second matrix. So we will have four multiplied by negative eight plus seven as the second element of that second row multiplied by nine, right, one more element to go. And that's gonna be the second row of the first matrix multiplied by the second column of the second matrix. So we get four multiplied by seven plus seven multiplied by 13. So now that we know all the values let's do the calculations. So starting in the top left corner, zero times anything is zero and I'm not going to add it in. So if I don't say it, it's because it's zero, negative two multiplied by negative eight is 16, continuing to the right negative two multiplied by seven is negative 14. First element in the second row of our solution matrix four multiplied by negative eight is negative 32. We're gonna add that to seven multiplied by nine, which is 63. And when we add those together, we get 31 next we have four multiplied by seven, which is 28 plus seven multiplied by 13, which is 91. And we add those together, we get 119. So our result is a two by two matrix where the top row is 16, negative 14. The second row is 31 119. And this matches answer choice C have a nice day.

Perform each operation, if possible.
$[\begin{matrix} - 1 & 0 \\ 2 & 5 \end{matrix}] [\begin{matrix} - 3 & 4 \\ 2 & 8 \end{matrix}]$

Key Concepts

Matrix Dimensions and Compatibility

Matrix Addition and Subtraction

Matrix Multiplication

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