Question

Find the sum of the matrices. $$ \left[\begin{array}{rr} 6.2 & -1.2 \\ -2.5 & -4.4 \\ 3.4 & -5.8 \end{array}\right]+\left[\begin{array}{rr} 1.5 & 9.2 \\ 6.6 & -2.2 \\ 5.7 & -7.1 \end{array}\right] $$

Short answer

The sum of the two matrices is:\[\begin{array}{r r}7.7 & 8 \4.1 & -6.6 \9.1 & -12.9 \end{array}\]

Step-by-step solution

Verify matrix dimensions

Examine both matrices to ensure they have the same dimensions. Here, both matrices are of size 3x2, so they can be added together.

Add corresponding entries

For each element in the same row and column position in both matrices, perform the addition operation. \[\begin{array}{r r}6.2 + 1.5 & -1.2 + 9.2 \-2.5 + 6.6 & -4.4 - 2.2 \3.4 + 5.7 & -5.8 - 7.1 \end{array}\]

Formulate the result

The result matrix is the sum of each corresponding element in the two matrices.\[\begin{array}{r r}7.7 & 8 \4.1 & -6.6 \9.1 & -12.9 \end{array}\]