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Natural Scientific 991 manual · Chapter 10 of 18

Matrices

Define matrices A to D up to 4×4, then add, multiply, invert, transpose and take determinants.

10.1Define a matrix#

Press MENU then 4 to open the Matrix app (MAT). Press OPTN and choose 1 (Define Matrix), then pick MatA to MatD, then the number of rows and columns (1 to 4). A form appears with one box per element: type a value and press = to go to the next one.

Example 10.1

Define MatA as 2×2

  1. Open Matrix. OPTN 1, MatA (1), 2 rows, 2 columns.

    MENU4OPTN1122

  2. Type the elements 1, 2, 3, 4 pressing equals after each.

    1=2=3=4=

  3. Type MatA with OPTN 3 and press equals.

    OPTN3=
Result of the example "Define MatA as 2×2" The display shows: MatA / [[1 2] / [3 4]].
You should see[[1 2] [3 4]]
The Matrix OPTN menu The display shows: 1:Define Matrix / 2:Edit Matrix / 3:MatA / 4:MatB.
The Matrix OPTN menu

10.2Edit a matrix you already defined#

OPTN 2 (Edit Matrix) reopens the form for a matrix, keeping the old values. Type over the ones you want to change; press = to accept each box.

Example 10.2

Change the first element

  1. Define MatA, then OPTN 2, MatA.

    MENU4OPTN11221=2=3=4=OPTN21

  2. Type 5 in the first box.

    5=
Result of the example "Change the first element" The display shows: MatA / MatA11=5 / MatA12=2 / MatA21=3.
You should seeMatA11=5 MatA12=2

10.3Add, multiply, square and invert matrices#

Use OPTN then 3 to 6 to insert MatA, MatB, MatC or MatD into a calculation, and then the usual keys. x² squares a matrix, x⁻¹ inverts it, and multiplying by a number multiplies every element. A matrix shown with elements in rows is the answer. The result is also stored in MatAns (OPTN 7).

Example 10.3

Multiply by a number

  1. Define MatA (1, 2, 3, 4).

    MENU4OPTN11221=2=3=4=

  2. MatA × 2.

    OPTN3×2=
Result of the example "Multiply by a number" The display shows: MatA×2 / [[2 4] / [6 8]].
You should see[[2 4] [6 8]]
Example 10.4

Multiply two matrices

  1. Define MatA.

    MENU4OPTN11221=2=3=4=

  2. MatA × MatA.

    OPTN3×OPTN3=
Result of the example "Multiply two matrices" The display shows: MatA×MatA / [[ 7 10] / [15 22]].
You should see15 22]]
Example 10.5

Square a matrix

  1. Define MatA, then MatA squared.

    MENU4OPTN11221=2=3=4=OPTN3x²=
Result of the example "Square a matrix" The display shows: MatA² / [[ 7 10] / [15 22]].
You should see15 22]]
Example 10.6

Inverse of a matrix

  1. Define MatA, then MatA to the power minus one.

    MENU4OPTN11221=2=3=4=OPTN3x⁻¹=
Result of the example "Inverse of a matrix" The display shows: MatA⁻¹ / [[ -2 1] / [1.5 -0.5]].
You should see-2 1.5 -0.5

10.4Determinant, transpose and identity#

OPTN numberItemMeaning
1Define MatrixChoose a matrix and its size.
2Edit MatrixChange a matrix.
3 to 6MatA to MatDInsert a matrix.
7MatAnsThe last matrix answer.
8DeterminantDet( of a square matrix.
9TranspositionTrn( swaps rows and columns.
10 (press up from the top)IdentityIdentity( builds an n by n identity matrix.
Example 10.7

Determinant

  1. Define MatA.

    MENU4OPTN11221=2=3=4=

  2. OPTN 8, MatA, bracket.

    OPTN8OPTN3)=
Result of the example "Determinant" The display shows: Det(MatA) / -2.
You should see-2
Example 10.8

Transpose

  1. Define MatA.

    MENU4OPTN11221=2=3=4=

  2. OPTN 9, MatA, bracket.

    OPTN9OPTN3)=
Result of the example "Transpose" The display shows: Trn(MatA) / [[1 3] / [2 4]].
You should see[[1 3] [2 4]]
Example 10.9

Identity matrix

  1. Press OPTN then up to jump to the last item, Identity, and choose it with equals. Type 3.

    MENU4OPTN▲=3)=
Result of the example "Identity matrix" The display shows: Identity(3) / [[1 0 0] / [0 1 0] / [0 0 1]].
You should see[[1 0 0] [0 1 0] [0 0 1]]
det⁡(abcd)=ad−bc\det\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bc
Determinant of a 2×2 matrix

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