Adding and Subtracting Matrices

Steps for adding and subtracting matrices. 

A^t means transpose.

When you transpose a matrix, you switch the rows with the columns and columns with the rows.  

Example: 

(6 7 8)

(8 0 2)

(2 8 1)

When transposed, it comes out as: 

(6 8 2)

(7 0 8)

(8 2 1)

The dimensions of a matrix is found by using rows by columns.

Example: 

The dimensions of the matrix in the first example would be 3 x 3. (There are 3 rows and 3 columns.)

When adding a matrix with another matrix, they must have the same dimensions.

When adding matrices, you have to add the corresponding entries with each other. 

Example:

(9 8)         (1 2)

(0 1)         (9 3)

A. What are the dimensions of the two matrices? 

Answer: 2x2 

B. Add the following matrices. 

Answer: (9 8) + (1 2) = (10 10)

             (0 1)    (9 3)    (9    4)