If \left[\begin{array}{ccc}1 & 2 & 1 \ 2 & 3 & 1 \ 3 & a & ...

CBSE Class 12 Math 2023 All Sets Solved Paper

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Question : 17 of 20

Marks: +1, -0

If

{[\table 1 , 2 , 1 ; 2 , 3 , 1 ; 3 , a , 1]}

is a non-singular matrix and a

∈

A , then the set A is:

$ℝ$
{0}
{4}
$ℝ$ - {4}

Solution:

Let P =

{[\table 1,2,1;2,3,1;3,a,1]}

| P | =

{|\table 1,2,1; 2,3,1; 3,a,1|} = {|\table 1,2,1; 1,1,0; 2 , a - 2, 0|}

{(\table R_2⟶ R_2⟶ R_1; R_3⟶ R_3-R_1)}

⇒ | P | = a - 4

But | P |

\ne

0

\Rightarrow

a

\ne

4

∴ a ∈ ℝ-\{4\}

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