Question

Find the sum of the matrices. $$ \left[\begin{array}{rr} 4 & -1 \\ -5 & -9 \end{array}\right]+\left[\begin{array}{rr} -6 & -3 \\ 2 & -3 \end{array}\right] $$

Short answer

The sum of the given matrices is \( \left[\begin{array}{rr} -2 & -4 \ -3 & -12 \end{array}\right] \)

Step-by-step solution

Identify Corresponding Elements

Matrix A and Matrix B are given as: \( A = \left[\begin{array}{rr} 4 & -1 \ -5 & -9 \end{array}\right] \) \( B = \left[\begin{array}{rr} -6 & -3 \ 2 & -3 \end{array}\right] \) In this case, the corresponding elements are (Aij, Bij), denoting the element in the ith row and jth column of the matrix. The corresponding pairs then are ((4,-6), (-1,-3)), for the first row, and ((-5,2), (-9,-3)), for the second row.

Add Corresponding Elements

We then add these pairs element-wise. This results in the following summed elements for the new matrix: \( (4 + -6, -1 + -3) \) for the first row, and \( (-5 + 2, -9 + -3) \) for the second row.

Form The Result Matrix

In the end, we sum up the corresponding elements and create a new matrix C where Cij = Aij + Bij. For this problem, the result is: \( C = \left[\begin{array}{rr} -2 & -4 \ -3 & -12 \end{array}\right] \)