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Linear Algebra Decoded
 

Linear Algebra Decoded Example

Linear Algebra Decoded
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This example has been taken directly from the solution given by Linear Algebra Decoded to the formulated problem.
Compute A+B where A and B are matrices defined as:

    ┌            ┐
    │  2  -3  -5 │
    │ -4   3   3 │
A = │  9   3   8 │
    │ -5  -9   6 │
    └            ┘
    ┌            ┐
    │  8   6   0 │
    │ -5  -5  -9 │
B = │  7  -5  -5 │
    │  1  -4   1 │
    └            ┘

How to solve this problem?
The sum of two matrices is defined when both matrices have equal size, and the result is a new matrix of equal size, where each entry is obtained by adding the entries at same position in both matrices. Matrices of different sizes cannot be added.

Step 1: Add the corresponding entries of the matrices A and B.

        ┌                                 ┐
        │     2 + 8     -3 + 6     -5 + 0 │
        │ -4 + (-5)   3 + (-5)   3 + (-9) │
A + B = │     9 + 7   3 + (-5)   8 + (-5) │
        │    -5 + 1  -9 + (-4)      6 + 1 │
        └                                 ┘

Step 2: Final solution.

        ┌             ┐
        │ 10    3  -5 │
        │ -9   -2  -6 │
A + B = │ 16   -2   3 │
        │ -4  -13   7 │
        └             ┘

  
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