TI-84 Plus CE field manual for IB Math

AI HL only · 38 of 45

Determinant and inverse of a matrix

AI HL

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

For C=⎣⎡210121012⎦⎤, find det(C) and C−1.

Press to open MATRIX, move to EDIT, choose 1:[A], set the dimensions to 3 x 3, and fill the rows 2, 1, 0, 1, 2, 1, and 0, 1, 2, pressing after each entry.

NORMALFLOATAUTOREALRADIANMP
MATRIX[A] 3 x3
210121012

Return to the home screen with . Open MATRIX again, move to MATH, choose 1:det(, then press to paste [A], close the parenthesis, and press .

NORMALFLOATAUTOREALRADIANMP
det([A])
4

The determinant is nonzero, so the inverse exists. Paste [A] again, press , then . The TI-84 shows the inverse entries as decimals, far quicker to trust than a 3×3 inverse worked by hand.

NORMALFLOATAUTOREALRADIANMP
det([A])
4
[A]−1
⎣⎡​0.75−0.50.25​−0.51−0.5​0.25−0.50.75​⎦⎤​

det(C)=4 and C−1=41⎣⎡3−21−24−21−23⎦⎤=⎣⎡43−2141−211−2141−2143⎦⎤.

Your turn

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

1
For A=⎣⎡211121112⎦⎤, find det(A) and A−1.
2
For B=⎣⎡310121012⎦⎤, find det(B) and B−1.
3
For C=⎣⎡102210031⎦⎤, find det(C) and C−1.