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How Do You Add and Subtract Matrices with Fractions and Decimals?

Given matrices A and B, find A+B and A-B. A=[8 10.6 B=[-12 1.75 1/8 3/2] 2/6 9]

Summary

  1. Pair each element in one matrix with the element in the same position in the other matrix
  2. To add the matrices, we need to add each pairing
  3. 9 is the same as 9 divided by 1, so you can add the last two as fractions
  4. After you've set up the subtraction matrix, all that's left is to perform the subtraction

Notes

    1. In order to add or subtract matrices, they MUST be the same size
    1. In order for us to add or subtract A and B, B will also have to be a 2x2 matrix
    1. This means that we can add or subtract B from A!
    1. A and B are both 2x2 matrices
    2. Which means that they both have 2 rows and 2 columns
    1. To add two matrices, you have to add each element from one matrix with its pair in the second matrix
    1. To add two matrices, you have to add each element from one matrix with its pair in the second matrix
    1. We've created pairs between the two matrices
    2. All that's left is to add each pairing!
    1. 8 and -12 are being added in the upper left element because they are the upper left pairing
    2. 10.6 and 1.75 are being added in the upper right element because they are the upper right pairing
    1. One eighth and two sixths are being added in the lower left element because they are the lower left pair
    2. Three halves and 9 are being added in the lower right element because they are the lower right pair
    1. Complete the addition for each individual element
    1. Since we're just simplifying addition, -4 takes the place of 8+(-12) in the first element
    1. Since we're just simplifying addition, 12.35 takes the place of 10.6+1.75 in the second element
    2. And 11 over 24 takes the place of the next element
    3. 21 over 2 is the last element
    4. Adding a fraction and a whole number is like adding two fractions with different denominators
    1. We've already done this step in when we added the matrix
    1. We've already done this step in when we added the matrix, so let's just use the pairs we already know
    1. The pairs we already know are:
    2. 8 and -12
    3. 10.6 and 1.75
    4. 1/8 and 2/6
    5. 3/2 and 9
    1. Remember, each pairing of elements will take the same position in our answer matrix
    1. The matrices HAVE to be the same size
    2. Each element in the first matrix must be paired with an element in the SAME position from the second matrix