For a real number

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

For a real number

t

, consider the matrix

T(t)=\begin{pmatrix}1 &t &t^{2}\\ 0 &1 &t\\ 0 &0 &1\end{pmatrix}.

(a) Compute

\det\bigl(T(t)\bigr)

in terms of

t

. (b) Hence find all real values of

t

for which

T(t)

is invertible. (c) For

t=1

, determine

T(1)^{-1}