Calculator Commands for Linear Algebra

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. 1. Write each equation in y = mx + b form.

2. 2. Insert equations in the y-menu.

3. 3. Graph the lines.

4. 4. Use the Intersection tool to get the answer.

To add or subtract matrices:

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

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

To multiply by a scalar:

1. 1. Insert the elements into the matrix A.

2. 2. With a new screen, press the scalar and multiply: k * [A], and press Enter.

To multiply two matrices together:

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

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

To switch rows:

1. 1. Insert the elements into a matrix.

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

To add two rows together:

1. 1. Insert the elements into a matrix.

2. 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. 1. Insert the elements into a matrix.

2. 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. 1. Insert the elements into a matrix.

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

To create an echelon form:

1. 1. Insert the elements into a matrix.

2. 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. 1. Insert the elements into a matrix.

2. 2. Use the caret operation with power, p: [matrix name] ^ p, and press Enter.

To find inverses:

1. 1. Insert the elements into a matrix.

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

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

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

4. 4. Press, A⁻¹ * B, and press Enter.

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