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How Do You Add Matrices?

Add the two matrices given in the diagram.

Summary

  1. You can only add matrices that have the same dimensions
  2. These matrices have the same dimensions, which means that we can add them
  3. You can only add elements that have corresponding positions
  4. 8 and -12 correspond
  5. 15 and 0 correspond
  6. 7 and 2 correspond
  7. -3 and -11 correspond
  8. The matrix we end up with when we add will have the same dimensions as the ones we started with: 2x2

Notes

    1. By dimensions we mean the number of rows and columns in each matrix
    1. A matrix with two rows and two columns is called a '2 by 2' or '2x2' matrix
    1. You can only add matrices that have the same dimensions
    2. Both of our matrices are 2x2 matrices, so we can add them!
    1. We say that an element in one matrix 'corresponds' to an element in the other if they're in the same position
    2. Each element in one matrix corresponds with an element in the other matrix
    3. You can only add elements that have corresponding positions
    1. Each element in one matrix corresponds to an element in the other matrix
    2. You can only add elements that have corresponding positions
    3. Positions are named by their row and column
    1. Each element in one matrix corresponds to an element in the other matrix
    2. You can only add elements that have corresponding positions
    3. Positions are named by their row and column
    1. An element corresponds with another element when they have the same position within their matrices
    2. 7 and 2 correspond because they are both in the second row and first column of their matrices
    3. -3 and -11 correspond because they are both in the second row and second column of their matrices
    1. You have to add the elements in their corresponding positions
    2. Positions are named by their row and column
    3. An element corresponds with another element when they have the same position within their matrices
    1. Now we just need to simplify each element of the new matrix
    1. Adding a negative number to a positive number is similar to doing subtraction
    2. Instead of adding that negative number, you can subtract a positive version of that number
    3. Adding two negative numbers together is like adding two positive numbers together, except the answer is negative!
    4. The final matrix has the same dimensions as the original matrices: it's also a 2x2 matrix