Let $$A = \left( {\matrix{ {[x + 1]} & {[x + 2]} & {[x + 3]} \cr {[x]} & {[x + 3]} & {[x + 3]} \cr {[x]} & {[x + 2]} & {[x + 4]} \cr } } \right)$$, 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 :
Solution
$$\left| {\matrix{
{[x + 1]} & {[x + 2]} & {[x + 3]} \cr
{[x]} & {[x + 3]} & {[x + 3]} \cr
{[x]} & {[x + 2]} & {[x + 4]} \cr
} } \right| = 192$$<br><br>R<sub>1</sub> $\to$ R<sub>1</sub> $-$ R<sub>3</sub> & R<sub>2</sub> $\to$ R<sub>2</sub> $-$ R<sub>3</sub><br><br>$$\left[ {\matrix{
1 & 0 & { - 1} \cr
0 & 1 & { - 1} \cr
{[x]} & {[x] + 2} & {[x] + 4} \cr
} } \right] = 192$$<br><br>$2[x] + 6 + [x] = 192 \Rightarrow [x] = 62$
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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