Perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D <math alttext="A equals the 2 by 3 matrix Row 1: 2 negative 1 2 Row 2: 5 3 negative 1 times B equals the 3 by 2 matrix Row 1: 0 negative 2 Row 2: 3 2 Row 3: 1 negative 5 times C equals the 3 by 3 matrix Row 1: 1 2 3 Row 2: negative 1 1 2 Row 3: negative 1 2 1 times D equals the 2 by 3 matrix Row 1: negative 2 3 1 Row 2: 3 negative 2 4" data-value="A=\begin{bmatrix}2 & -1 & 2\\ 5 & 3 & -1\end{bmatrix}\quad B=\begin{bmatrix}0 & -2\\ 3 & 2\\ 1 & -5\end{bmatrix}C=\begin{bmatrix}1 & 2 & 3\\ -1 & 1 & 2\\ -1 & 2 & 1\end{bmatrix}\quad D=\begin{bmatrix}-2 & 3 & 1\\ 3 & -2 & 4\end{bmatrix}"> A = [ 2 − 1 2 5 3 − 1 ] B = [ 0 − 2 3 2 1 − 5 ] C = [ 1 2 3 − 1 1 2 − 1 2 1 ] D = [ − 2 3 1 3 − 2 4 ] A=\begin{bmatrix}2 & -1 & 2\\ 5 & 3 & -1\end{bmatrix}\quad B=\begin{bmatrix}0 & -2\\ 3 & 2\\ 1 & -5\end{bmatrix}C=\begin{bmatrix}1 & 2 & 3\\ -1 & 1 & 2\\ -1 & 2 & 1\end{bmatrix}\quad D=\begin{bmatrix}-2 & 3 & 1\\ 3 & -2 & 4\end{bmatrix}

Welcome back. I'm so glad you're here. We've got two matrices A and B. And we are to perform the mentioned operation. Well, in this case it is A plus B. And we can designate A as red and be as blue. And what we're going to do to add these two matrices together is find the ones that are in the corresponding positions. So the upper left, we've got to And we're going to add the one in the upper left of B. -4. And now we can look back at A and we can look at the upper right of A. That's three. And we'll add the upper right of B, which is also three. Now we can look at the lower left of A. Which is eight and we can add the lower left of B which is one. And we can look at the lower right of A. Which is seven and we can add the lower right of B which is two. Now we just perform the addition. So two plus negative four. Well, that's negative 23 plus three is 68 plus one is nine and seven plus two is nine. We look at our answer choices and that matches with answer choice C. Well done, we'll catch you on the next one

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

1:37 minutes

Problem 14

Textbook Question

Perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D
$A = [\begin{matrix} 2 & - 1 & 2 \\ 5 & 3 & - 1 \end{matrix}]$

Verified step by step guidance

Identify the dimensions of matrices A and D. To add two matrices, they must have the same number of rows and the same number of columns.

Check if the number of rows in matrix A equals the number of rows in matrix D, and the number of columns in matrix A equals the number of columns in matrix D.

If the dimensions match, proceed to add the corresponding elements of matrices A and D. This means adding each element in row i, column j of A to the element in row i, column j of D.

Write the resulting matrix where each element is the sum of the corresponding elements from A and D, i.e., $C_{ij} = A_{ij} + D_{ij}$ for all i and j.

If the dimensions do not match, state that the addition is not defined because matrix addition requires matrices to be of the same size.

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 Addition

Matrix addition involves adding corresponding elements of two matrices of the same dimensions. Both matrices must have the same number of rows and columns for the operation to be defined. The result is a new matrix where each element is the sum of the elements from the original matrices.

Matrix Dimensions and Compatibility

The dimensions of a matrix are given by its number of rows and columns. For operations like addition or subtraction, matrices must have identical dimensions. Understanding matrix size is crucial to determine whether an operation is defined or not.

Undefined Matrix Operations

Some matrix operations are undefined if the matrices involved do not meet specific criteria, such as matching dimensions for addition. Recognizing when an operation cannot be performed is important to avoid errors and correctly interpret the problem.

Watch next

Master Introduction to Matrices with a bite sized video explanation from Patrick

Start learning