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Precalculus

Matrix determinant and inverse

Find the determinant and inverse of [[1, 2], [3, 4]].

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For a 2 × 2 matrix [[a, b], [c, d]] the determinant is ad − bc. For [[1, 2], [3, 4]] that is 1×4 − 2×3 = −2.

The inverse is [[-2, 1], [1.5, -0.5]]. A matrix with determinant 0 has no inverse.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. Store the matrix in [A] as in the matrices guide.

    2nd[×2nd[×1,22nd]−2nd[×3,42nd]−2nd]−sto→2ndMATRIXx⁻¹1enter

  2. Determinant: open the matrix menu (2nd, x⁻¹), move right to MATH, pick 1 det(, then [A] and close the bracket.

    2ndMATRIXx⁻¹▶12ndMATRIXx⁻¹1)enter

  3. Inverse: [A], then the x⁻¹ key.

    2ndMATRIXx⁻¹1x⁻¹enter

You should seedet([A]) ⁻2 [[ ⁻2 1] [1.5 ⁻.5]]

Classic Graphing 84 key reference

Natural Scientific 991 · Determinant

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Define MatA in the Matrix app, as in the matrices guide.

    MENU4OPTN11221=2=3=4=

  2. OPTN 8 is the determinant. Then OPTN 3 for MatA, a bracket and =.

    OPTN8OPTN3)=

You should seeDet(MatA) -2

Natural Scientific 991 key reference

Natural Scientific 991 · Inverse

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Define MatA in the Matrix app.

    MENU4OPTN11221=2=3=4=

  2. Insert MatA (OPTN 3), press the x⁻¹ key, then =.

    OPTN3x⁻¹=

You should see[[ -2 1] [1.5 -0.5]]

Natural Scientific 991 key reference

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

  1. Fill Mat A on the Run-Matrix screen (F3 MAT).

    F3EXE▼▼EXE1EXE2EXE3EXE4EXEEXITEXIT

  2. Determinant: OPTN, F2 (MAT), F4 (Det), F1 (Mat A), EXE.

    OPTNF2F4F1EXE

You should seeDet Mat A -2

Natural Color Graphing key reference

Natural Color Graphing · Inverse

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

  1. Fill Mat A on the Run-Matrix screen (F3 MAT).

    F3EXE▼▼EXE1EXE2EXE3EXE4EXEEXITEXIT

  2. OPTN, F2 (MAT), F1 (Mat A), then SHIFT and the ) key for x⁻¹, and EXE.

    OPTNF2F1SHIFTx⁻¹)EXE

You should see[[ -2 1] [1.5 -0.5]]

Natural Color Graphing key reference

Classic CAS · Determinant

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Open the menu and pick 7 (Matrix & Vector), then 2 (det). Type the matrix and close the bracket.

    menu72ctrl[(1,2ctrl;,3,4ctrl]))enter

You should seedet([1,2;3,4]) -2

Classic CAS key reference

Classic CAS · Inverse

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Type the matrix, then ^ and −1. Press the right arrow and enter.

    ctrl[(1,2ctrl;,3,4ctrl])^(−)1▶enter

You should see[[-2,1][3/2,-1/2]]

Classic CAS key reference

RPN Advanced 42 · Determinant

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

  1. Build the matrix as in the matrices guide.

    2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXIT

  2. Press the third menu key (DET).

    √x

You should seex: -2.0000

RPN Advanced 42 key reference

RPN Advanced 42 · Inverse

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

  1. Build the matrix as in the matrices guide.

    2ENTER2⇧MATRIX9Σ+XEQ1LN2LN3LN4EXIT

  2. Press the second menu key (INV), then EDIT (the last menu key) to read the first entry, -2.

    1/xXEQ

You should see1:1=-2.0000

RPN Advanced 42 key reference

RPN Power 48

Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.

  1. Type the matrix and press ENTER, as in the matrices guide.

    ◀[ ]9◀[ ]91SPC2▶▶SPC◀[ ]93SPC4ENTER

  2. Open the APPS menus and pick MATRX (the fourth menu key). Then DET is the third key.

    APPSF4F3

You should see-2

The fourth menu key, INV, gives the inverse [[ -2 1 ] [ 1.5 -.5 ]] instead.

RPN Power 48 key reference

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