The value of $$\left| {\matrix{ {(a + 1)(a + 2)} & {a + 2} & 1 \cr {(a + 2)(a + 3)} & {a + 3} & 1 \cr {(a + 3)(a + 4)} & {a + 4} & 1 \cr } } \right|$$ is :
Solution
Given, $\Delta$ = $$\left| {\matrix{
{(a + 1)(a + 2)} & {a + 2} & 1 \cr
{(a + 2)(a + 3)} & {a + 3} & 1 \cr
{(a + 3)(a + 4)} & {a + 4} & 1 \cr
} } \right|$$
<br><br>R<sub>2</sub> $\to$ R<sub>2</sub> $-$ R<sub>1</sub> and R<sub>3</sub> $\to$ R<sub>3</sub> $-$ R<sub>1</sub><br><br>$\Delta$ = $$\left| {\matrix{
{(a + 1)(a + 2)} & {a + 2} & 1 \cr
{(a + 2)(a + 3 - a - 1)} & 1 & 0 \cr
{{a^2} + 7a + 12 - {a^2} - 3a - 2} & 2 & 0 \cr
} } \right|$$<br><br>$$ = \left| {\matrix{
{{a^2} + 3a + 2} & {a + 2} & 1 \cr
{2(a + 2)} & 1 & 0 \cr
{4a + 10} & 2 & 0 \cr
} } \right|$$<br><br>$= 4(a + 2) - 4a - 10$<br><br>$= 4a + 8 - 4a - 10 = - 2$
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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