Dawnbridge

TI-Nspire CX II field manual for IB Math

AI HL only · 38 of 45

38

Determinant and inverse of a matrix

AI HL

Enter a matrix A, compute detA to confirm it is invertible, then compute A−1.

Goal

For ​C=⎣⎡​210​121​012​⎦⎤​, find ​det(C)​ and ​C−1.

1

Store the matrix: type c:= with , insert a 3 x 3 matrix template with → 7: Matrix & Vector → 1: Create → 1: Matrix — in the dialog, type to set the rows and columns ( moves between the fields; the arrows change the numbers instead). Fill the entries 2, 1, 0, 1, 2, 1, 0, 1, 2 (move between cells with ), and press .

Scratchpad
RAD
c:=⎣⎡​210​121​012​⎦⎤​
⎣⎡​210​121​012​⎦⎤​
2

Compute the determinant: press → 7: Matrix & Vector → 3: Determinant to paste det(, type , and press .

Scratchpad
RAD
det(c)
4
3

The determinant is nonzero, so the inverse exists. Type , raise it to the power ​−1​ (press then ), and press . The Nspire returns the inverse with exact fractional entries.

Scratchpad
RAD
det(c)
4
c−1
⎣⎡​43​−21​41​​−21​1−21​​41​−21​43​​⎦⎤​
Result

​det(C)=4​ and ​C−1=41​⎣⎡​3−21​−24−2​1−23​⎦⎤​=⎣⎡​43​−21​41​​−21​1−21​​41​−21​43​​⎦⎤​.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    For ​A=⎣⎡​211​121​112​⎦⎤​, find ​det(A)​ and ​A−1.

  2. 2

    For ​B=⎣⎡​310​121​012​⎦⎤​, find ​det(B)​ and ​B−1.

  3. 3

    For ​C=⎣⎡​102​210​031​⎦⎤​, find ​det(C)​ and ​C−1.