Matrix Definitions

Let A be a matrix with m rows and n columns.  The element of A from the i'th row and j'th column is written a_ij  

• The matrix A is called square if m = n.  

• If A is a m by n matrix with general element a_ij and B is a m by n matrix with general element b_ij then we define the sum of A and B by A + B having the ij^th  element a_ij + b_ij.  

• If A is a m by n matrix with general element a_ij and B is a m by n matrix with general element b_ij then we define the difference of A and B by A - B having the ij^th  element a_ij - b_ij.  

• If A is a matrix and c is a constant then the matrix cA has general element ca_ij 

• If A is a m by n matrix the the transpose of A, written  A^T (read "A transpose")  is the n by m matrix with general element a^T_ij   = a_ji.  In other words the rows of the transpose are the columns of the original matrix.

• A matrix is called square if n = m, that is, the number of rows equals the number of columns.

• A matrix square matrix A is called a diagonal matrix if a_ij = 0 for i not equal to j.  In other word a diagonal matrix is zero everywhere off the diagonal.

• A square matrix A is called upper triangular if a_ij = 0 for i > j.  An upper triangular matrix has all zeros below the diagonal.

• A square matrix A is called lower triangular if a_ij = 0 for i < j.  A lower triangular matrix has all zeros above the diagonal.

• A matrix A is called a scalar matrix if it is diagonal and all the diagonal entries are equal to each other.

• A matrix is called the identity matrix (written as I) if it is a scalar matrix with diagonal entry 1.

Matrices and The TI 85 Calculator

To enter a matrix into the calculator

1. Hit the Matrix button which is second 7. 

2. Hit Edit which is F2. 

3. Type a name such as "A" and hit enter.

4. Type in the number of rows for the matrix and hit enter.

5. Type in the number of columns for the matrix and hit enter.

6. Now type in the entries of the matrix.  For example 1,3 = 2 means that 2 is in the first row and the third column.

7. Hit the Exit key.

Some Operations of matrices.

1. To Multiply matrices, use the multiplication key.  A*B

2. To add or subtract, use the + and - keys as with real numbers.

3. To find the inverse of a matrix use the x^-1 key.  A^-1

4. To find the determinate of a matrix, hit the Matrix key, then hit F3 (Math), then hit F1 (det), then hit the name of the matrix.