# Perform Matrix Arithmetic on the TI-83 Plus

When evaluating arithmetic expressions that involve matrices on the TI-3 Plus graphing calculator, you usually want to perform the following basic operations: scalar multiplication, negation (additive inverse), addition, subtraction, multiplication, and inversion (multiplicative inverse). You may also want to raise a matrix to an integral power or find its transpose. And you may want to use the identity matrix in an arithmetic expression.

Here’s how you enter matrix operations in an arithmetic expression:

Define the matrices in the Matrix editor.

Press [2nd[MODE] to access the Home screen.

All matrix operations are performed on the Home screen.

If you want to clear the Home screen, repeatedly press [CLEAR].

Enter the operations you want to perform and press [ENTER] when you’re finished.

As with algebraic expressions, the Home screen is where you evaluate arithmetic expressions that involve matrices. To paste the name of a matrix into an expression, press

**[2nd][**and key in the number of the matrix name. Here’s how you enter the various operations into the arithmetic expression:*x*^{–1}]**Entering the scalar multiple of a matrix:**To enter the scalar multiple of a matrix in an arithmetic expression, enter the value of the scalar and then enter the name of the matrix.

**Negating a matrix:**To negate a matrix, press

**[(-)]**and then enter the name of the matrix.**Entering the identity matrix:**You don’t have to define an identity matrix in the Matrix editor in order to use it in an algebraic expression. To enter an identity matrix in an expression, press

to select the

**identity**command from the Matrix Math menu. Then enter the size of the identity matrix. For example, enter**2**for the 2 X 2 identity matrix.**Adding or subtracting matrices:**When adding or subtracting matrices, the matrices must have the same dimensions. If they don’t, you will get the ERR: DIM MISMATCH error message.

Entering the addition and subtraction of matrices is straightforward; just combine the matrices by pressing

**[+]**or**[–]**, as appropriate.**Multiplying two matrices:**When finding the product A*B of two matrices, the number of columns in the first matrix A must equal the number or rows in the second matrix B. If this condition isn’t satisfied, you will get the ERR: DIM MISMATCH error message.

The multiplication of matrices is straightforward; just indicate the product by using juxtaposition by pressing

**[x]**.**Finding the inverse of a matrix:**When finding the inverse of a matrix, the matrix must be

*square*(number of rows = number of columns) and*nonsingular*(nonzero determinant). If it is not square, you will get the ERR: INVALID DIM error message. If is singular (determinant = 0), you will get the ERR: SINGULAR MAT error message.Entering the inverse of a matrix is straightforward; just enter the name of the matrix and then press

**[**.*x*^{–1}][WINDOW]**Raising a matrix to a positive integral power.**When finding the power of a matrix, the matrix must be square. If it isn’t, you will get the ERR: INVALID DIM error message.

Only non-negative integers can be used for the power of a matrix. If the exponent isn’t a nonnegative integer, you will get the ERR: DATA TYPE error message. If you raise a square matrix to the zero power, you will get the identity matrix.

To raise a square matrix to a negative power, raise the inverse of the matrix to the corresponding positive power.

Entering the positive power of a matrix is straightforward; just enter the name of the matrix, press

**[^]**, and enter the power.**Transposing of a matrix.**To transpose a matrix in an arithmetic expression, enter the name of the matrix and then press

to select the Transpose command from the Matrix Math menu.