Matrix operation rules
key notes:
✈️ Matrices can be added only if their dimensions are exactly the same.
✈️ Matrices can be subtracted only if their dimensions are exactly the same.
✈️ Two matrices can be multiplied only if the number of columns in the first matrix is equal to the number of rows in the second matrix.
✈️ The product of a number with a matrix has the same number of rows and columns as the original matrix.
✈️ Any matrix can always be multiplied by any number, regardless of its dimensions.
✈️ The product AB of two matrices has the same number of rows as A and the same number of columns as B.
✈️ When writing the dimensions, put the number of rows before the number of columns.
Learn with an example
👉 What are the dimensions of matrix H?
_____ by _____
The first matrix in the product has 1 row, so the product H also has 1 row. The second matrix in the product has 1 column, so H also has 1 column.
The dimensions of H are 1 by 1.
👉 Is this product defined?
7 [ 2 0 1 ]
- yes
- no
- This expression is the product of 7 and a matrix:
- 7 [ 2 0 1 ]
- The product of any number and any matrix is always defined.
👉 Is this product defined?
- yes
- no
- The first matrix has 3 columns:
- The second matrix has 3 rows:
- Since the number of columns in the first matrix is equal to the number of rows in the second matrix, the product of the two matrices is defined.
let’s practice! 🖊️
