# Calculator Commands for Linear Algebra

### Part of the Linear Algebra For Dummies Cheat Sheet

Graphing calculators are wonderful tools for helping you solve linear algebra processes; they allow you to drain battery power rather than brain power. Since there is a wide variety of graphing calculators out there, the following are general instructions for help with linear algebra that apply to most graphing calculators:

## To solve systems of equations by graphing:

1. Write each equation in

*y*=*mx*+*b*form.2. Insert equations in the

*y*-menu.3. Graph the lines.

4. Use the Intersection tool to get the answer.

## To add or subtract matrices:

1. Insert the elements into the matrices A and B.

2. With a new screen, press [A] + [B] or [A] – [B], and press Enter.

## To multiply by a scalar:

1. Insert the elements into the matrix A.

2. With a new screen, press the scalar and multiply:

*k** [A], and press Enter.

## To multiply two matrices together:

1. Insert the elements into the matrices A and B.

2. With a new screen, press [A] * [B], and press Enter.

## To switch rows:

1. Insert the elements into a matrix.

2. Use

*row swap*:*rowSwap*([matrix name], first row, second row), and press Enter.

## To add two rows together:

1. Insert the elements into a matrix.

2. Use

*row addition*: "*row*+", ([matrix name], row to be added to target row, target row), and press Enter.

## To add the multiple of one row to another:

1. Insert the elements into a matrix.

2. Use row

*sum*-*of*-*multiple*: "**row*+", (multiplier, [matrix name], row being multiplied, target row having multiple added to it), and press Enter.

## To multiply a row by a scalar:

1. Insert the elements into a matrix.

2. Use

*row**multiple*: "*row" (multiplier, [matrix name], row), and press Enter.

## To create an echelon form:

1. Insert the elements into a matrix.

2. Use

*row*-*echelon**form*:*ref*([matrix name]) or*reduced row-echelon form: rref*([matrix name]), and press Enter.

## To raise a matrix to a power:

1. Insert the elements into a matrix.

2. Use the caret operation with power,

*p*: [matrix name] ^*p*, and press Enter.

## To find inverses:

1. Insert the elements into a matrix.

2. Use the reciprocal operation,

*x*^{−1}: [matrix name]^{−1}, and press Enter.

## To solve systems of linear equations:

(This only works when the system has a single solution; it fails when the matrix A is singular.)

1. Write each equation with the variables in the same order and the constant on the other side of the equation sign.

2. Create a matrix A, whose elements are the coefficients of the variables.

3. Create a matrix B, whose elements are the constants.

4. Press, A

^{−1}* B, and press Enter.

The resulting vector has the values of the variables, in order.