Find each sum or difference, if possible. [ 6 − 9 2 4 1 3 ] + [ − 8 2 5 6 − 3 4 ] \left[ \begin{matrix} 6 & -9 & 2 \\ 4 & 1 & 3 \end{matrix} \right] + \left[ \begin{matrix} -8 & 2 & 5 \\ 6 & -3 & 4 \end{matrix} \right]

Hello, everyone. We are asked to calculate the sum for the given matrices. If possible, the matrices we are given are both two by three matrices. The first one has a first row of five negative 10 in the second row of three negative 17. The second matrix has a first row of 2023. In the second row of 17 76, our answer choices are a, a two by three matrix where the top row is seven negative 26. And the second row is 20 negative 6 B two by three matrix with the top row of seven negative 10 20 in the bottom row 13 C A two by three matrix with the top row of seven negative 10 26. The bottom row 26 13 or D, the sum does not exist first recall when adding or subtracting matrices, they have to have the same dimensions. So in this case, we have a two by three matrix added to a two by three matrix. So as they have the same dimensions check, we know we can add these. Our result is going to also be a two by three matrix and we are gonna add corresponding elements together. So starting in the top left corner, we would have the element five plus the element of two. The next would give us negative 10 plus zero. And next going horizontally, it would be three plus 23. Our second row starting from the left B three plus 17, negative one plus seven and seven plus six. Simplifying that I get seven negative 10 26 as my first row, 26 13 as my second row. And that matrix is my solution and it matches answer choice C have a nice day.

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

College Algebra

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

2:39 minutes

Problem 27

Textbook Question

Find each sum or difference, if possible.
$[\begin{matrix} 6 & - 9 & 2 \\ 4 & 1 & 3 \end{matrix}] + [\begin{matrix} - 8 & 2 & 5 \\ 6 & - 3 & 4 \end{matrix}]$

Verified step by step guidance

Identify the dimensions of both matrices to ensure they are the same. Since both are 2x3 matrices, addition or subtraction is possible.

Recall that matrix addition (or subtraction) is performed element-wise. This means you add (or subtract) corresponding elements from each matrix.

Write down the general formula for matrix addition: if $A = [a_{ij}]$ and $B = [b_{ij}]$, then $A + B = [a_{ij} + b_{ij}]$ for all $i$ and $j$.

Add the corresponding elements from each matrix. For example, add the element in the first row and first column of the first matrix to the element in the first row and first column of the second matrix, and continue this for all elements.

After performing the element-wise addition, write the resulting matrix with the sums in their respective positions to complete the solution.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Matrix Dimensions and Compatibility

Matrix addition or subtraction requires both matrices to have the same dimensions, meaning the same number of rows and columns. If the matrices differ in size, their sum or difference is undefined. Understanding this ensures that operations are only performed on compatible matrices.

Matrix Addition and Subtraction

To add or subtract matrices, you perform the operation element-wise, combining corresponding entries from each matrix. For example, the element in the first row and first column of the result is the sum or difference of the elements in the first row and first column of the original matrices.

Notation and Representation of Matrices

Matrices are typically represented as rectangular arrays enclosed in brackets, with rows and columns clearly defined. Understanding how to read and write matrices correctly is essential for performing operations and interpreting results in algebra.

Watch next

Master Determinants of 2×2 Matrices with a bite sized video explanation from Patrick

Start learning