Question

Find the sum or difference of the matrices. $$\left[\begin{array}{rr} -2 & 7 \\ 0 & 4 \end{array}\right]+\left[\begin{array}{rr} 3 & -6 \\ -1 & -5 \end{array}\right]$$

Short answer

The sum of the given matrices is [[1, 1], [-1, -1]].

Step-by-step solution

Understand Matrix Addition

In matrix addition, corresponding elements from each matrix are added together to form a new matrix. This means the element in the first row and first column of the first matrix is added to the element in the first row and first column of the second matrix. This process is repeated for all elements in the matrices.

Add corresponding elements

Now start adding elements from the given matrices. Starting from the first row first column, (-2) from the first matrix plus 3 from the second matrix equals 1. Then move to the first row second column, 7 from the first matrix added to (-6) from the second matrix equals 1. Continue this process for all elements in the matrices.

Create Result Matrix

Record the results obtained to form the resulting matrix. When we have added the corresponding elements from both matrices, the resulting matrix can be written as: \[ \left[\begin{array}{rr} 1 & 1 \ -1 & -1 \end{array}\right] \]