Consider the matrix B(t)= pmatrix t+2 & 3 4 & t-1 pmatrix

MATHEMATICS · Multi-part · CBSE · Mathematics · Determinants · Determinants

Problem

Consider the matrix

B(t)=\begin{pmatrix}t+2 & 3\\4 & t-1\end{pmatrix},

where

t\in\mathbb Z

. (i) Obtain

\det\bigl(B(t)\bigr)

as a polynomial in

t

. (ii) Find all integers

t

with

-5\le t\le5

for which

B(t)

is invertible.