Matrices and vectors

10.1The MATRIX menu#

Open MATRIX with shift 9. A matrix is one value on the stack, shown as [ 2×2 Matrix ]. You can store it in a register or a named variable. Entries are real numbers.

10.2Create and edit a matrix#

NEW makes a zero matrix, and EDIT opens it in the matrix editor. The top line shows row:column=value. Type a number and press the right-arrow menu key (→) to store it and move on. ENTER does the same as →: it stores the number and moves to the next element (after the last element it wraps to the first). Press EXIT to leave the editor; your edits are kept.

The ▲ and ▼ keys also move between rows. Moving past the last cell wraps around to the first.

Example 10.1

Build [[1, 2], [3, 4]]

1. Type 2, ENTER, 2 and press NEW (first key).

   2ENTER2⇧MATRIX9Σ+

2. Press EDIT (sixth key). Type each number and press → (fifth key); type the last number and EXIT.

   XEQ1LN2LN3LN4EXIT

   

Example 10.2

Check the editor shows the values

1. After building the matrix, open EDIT again and move right.

   2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXITXEQLN

10.3Determinant, inverse and transpose#

Example 10.3

Determinant of [[1,2],[3,4]]

1. Build the matrix and press DET (third key).

   2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXIT√x

Example 10.4

Inverse: look at the first entry

1. Build the matrix and press INV (second key).

   2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXIT1/x

2. Open the editor to read it: the first value is −2.

   XEQ

   

Example 10.5

Transpose

1. Build the matrix and press TRN (fourth key); the entry at 1:2 is now 3.

   2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXITLOGXEQLN

10.4Add, multiply and scale matrices#

The ordinary operations work on matrices: + and − need matrices of the same size, × multiplies a matrix by a number or by a matrix with matching inner size, and ÷ solves a linear system when Y is the right-hand side matrix and X the coefficient matrix.

Example 10.6

Square a matrix

1. Build [[1,2],[3,4]], duplicate it with ENTER and multiply.

   2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXITEXITEXITENTER×⇧MATRIX9XEQ

Example 10.7

Multiply by a number

1. The first entry of 2 times the matrix is 2.

   2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXITEXITEXIT2×⇧MATRIX9XEQ

10.5Solve a system of equations#

SIMQ solves $A\mathbf{x}=\mathbf{b}$. Type the number of equations and press SMQ. The menu offers A (coefficients), B (right-hand sides) and X (the answer). Edit A and B, then press X to compute and show the solution.

Example 10.8

Solve x + y = 3 and x − y = 1

1. Type 2 and press SIMQ (fifth key). Edit matrix A (first key): 1, 1, 1, −1.

   2⇧MATRIX9LNΣ+1LN1LN1LN1+/−EXIT

   

2. Edit B (second key): 3 and 1.

   1/x3LN1EXIT

3. Press X (third key). The editor shows x in row 1.

   √x

10.6Dot product, cross product and unit vectors#

A vector is a matrix with one row or one column. DOT needs two vectors of the same length. CRS needs two vectors of length 3. UVC divides a vector by its length.

Example 10.9

Dot product of (1,0,0) and (0,1,0)

1. Build both vectors with NEW 1 × 3 and EDIT.

   1ENTER3⇧MATRIX9Σ+XEQ1LN0LN0EXITEXITEXIT1ENTER3⇧MATRIX9Σ+XEQ0LN1LN0EXIT

2. Open page 2 and press DOT.

   ▼Σ+

Example 10.10

Unit vector of (3, 4)

1. Build the vector, open page 2 and press UVC (third key).

   1ENTER2⇧MATRIX9Σ+XEQ3LN4EXIT▼√x

2. Open the editor: the first value is 0.6.

   ⇧MATRIX9XEQ

10.7Name and store matrices#

DIM (page 2, fourth key) makes a named matrix of Y rows and X columns. EDN opens a named matrix for editing. A matrix can also be stored with STO into a register or variable, and recalled with RCL.

Example 10.11

Make a named 2 by 3 matrix

1. Type 2, ENTER, 3, open page 2 and press DIM. Type M (group J K L M, fourth key) and ENTER.

   2ENTER3⇧MATRIX9▼LOG√xLOGENTER

2. Recall it.

   EXITRCL⇧ALPHAENTER√xLOGENTER

Example 10.12

Store a matrix in a register

1. Build [[1,2],[3,4]], store it in register 00 and recall it.

   2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXITSTO000RCL00