Question

Perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+DA=[2−1253−1]B=[0−2321−5]C=[123−112−121]D=[−2313−24]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}

Accepted Answer

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.

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

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Key Concepts

Matrix Addition

Matrix Dimensions and Compatibility

Undefined Matrix Operations