SATHEE: Matrices and Determinants 3 Question 12

Matrices and Determinants 3 Question 12

14. Let $M$ be a $2 \times 2$ symmetric matrix with integer entries. Then, $M$ is invertible, if

(2014 Adv.)

(a) the first column of $M$ is the transpose of the second row of $M$

(b) the second row of $M$ is the transpose of the first column of $M$

(d) the product of entries in the main diagonal of $M$ is not the square of an integer

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Answer:

Correct Answer: 14. (c,d)

Solution:

PLAN: A square matrix $M$ is invertible, if dem $(M)$ or $| M | \neq 0$ .

Let $M =$ $[\begin{matrix} a & b \\ b & c \end{matrix}]$

(a) Given, $\frac{a}{b} =_{c}^{b} \Rightarrow a = b = c = α$

$\Rightarrow M = [\begin{matrix} α & α \\ α & α \end{matrix}] \Rightarrow | M | = 0 \Rightarrow M$ is non-invertible.

(b) Given, $[b c] = [a b]$

$\Rightarrow a = b = c = α$

Again, $| M | = 0$

$\Rightarrow M$ is non-invertible.

$\Rightarrow M$ is invertible.

$[∵ a$ and $c$ are non-zero]

(d) $M = [\begin{matrix} a & b \\ b & c \end{matrix}] \Rightarrow | M | = a c - b^{2} \neq 0$

$∵ a c$ is not equal to square of an integer.

$M$ is invertible.

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Matrices and Determinants 3 Question 12

14. Let $M$ be a $2 \times 2$ symmetric matrix with integer entries. Then, $M$ is invertible, if

Answer:

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

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सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Matrices and Determinants 3 Question 12

14. Let M be a 2×2 symmetric matrix with integer entries. Then, M is invertible, if

Answer:

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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14. Let $M$ be a $2 \times 2$ symmetric matrix with integer entries. Then, $M$ is invertible, if