SATHEE: Matrices and Determinants 3 Question 13

Matrices and Determinants 3 Question 13

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15. If the adjoint of a $3 \times 3$ matrix $P$ is $2 1 7$ , then the $\begin{array}{lll} 1 & 1 & 3 \end{array}$ possible value(s) of the determinant of $P$ is/are

======= ####15. If the adjoint of a $3 \times 3$ matrix $P$ is $2 1 7$ , then the $[\begin{matrix} 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \end{matrix}]$ possible value(s) of the determinant of $P$ is/are

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed

(a) -2

(b) -1

(d) 2

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Answer:

Correct Answer: 15. (a,d)

Solution:

PLAN: If $| A_{n \times n} | = Δ$ , then $| adj A | = Δ^{A - 1}$

Here, adj $P_{3 \times 3} =$ $[\begin{matrix} 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \end{matrix}]$

$\Rightarrow | adj P | = | P |^{2}$

$\begin{aligned} ∴ | adj P | & = [\begin{array}{c} 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \end{array}] = 1 (3 - 7) - 4 (6 - 7) + 4 (2 - 1) \\ = - 4 + 4 + 4 = 4 \Rightarrow | P | = \pm 2 \end{aligned}$

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Matrices and Determinants 3 Question 13

15. If the adjoint of a 3×3 matrix P is 217, then the 113 possible value(s) of the determinant of P is/are

Answer:

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15. If the adjoint of a $3 \times 3$ matrix $P$ is $2 1 7$ , then the $\begin{array}{lll} 1 & 1 & 3 \end{array}$ possible value(s) of the determinant of $P$ is/are