Let [A = ( pmatrix [x + 1] & [x + 2] & [x + 3] [x] & [x + 3] & [x + 3] [x] & [x + 2] & [x …

Question

Let $$A = \left( {\begin{pmatrix} {[x + 1]} & {[x + 2]} & {[x + 3]}  \
   {[x]} & {[x + 3]} & {[x + 3]}  \
   {[x]} & {[x + 2]} & {[x + 4]}  \ \end{pmatrix} } \right)$$, where [t] denotes the greatest integer less than or equal to t. If det(A) = 192, then the set of values of x is the interval :

Accepted Answer

$$\left| {\begin{pmatrix} {[x + 1]} & {[x + 2]} & {[x + 3]}  \
   {[x]} & {[x + 3]} & {[x + 3]}  \
   {[x]} & {[x + 2]} & {[x + 4]}  \

\end{pmatrix} } \right| = 192$$

R1 $$\to$$ R1 - R3 \& R2 $$\to$$ R2 - R3

$$\left[ {\begin{pmatrix} 1 & 0 & { - 1}  \
   0 & 1 & { - 1}  \
   {[x]} & {[x] + 2} & {[x] + 4}  \

\end{pmatrix} } \right] = 192$$

$$2[x] + 6 + [x] = 192 \Rightarrow [x] = 62$$

Solutions · 1