Download Orthogonal Matrix MCQs Free PDF

Orthogonal Matrix MCQ Quiz in বাংলা - Objective Question with Answer for Orthogonal Matrix - বিনামূল্যে ডাউনলোড করুন [PDF]

Last updated on Jul 3, 2025

পাওয়া Orthogonal Matrix उत्तरे आणि तपशीलवार उपायांसह एकाधिक निवड प्रश्न (MCQ क्विझ). এই বিনামূল্যে ডাউনলোড করুন Orthogonal Matrix MCQ কুইজ পিডিএফ এবং আপনার আসন্ন পরীক্ষার জন্য প্রস্তুত করুন যেমন ব্যাঙ্কিং, এসএসসি, রেলওয়ে, ইউপিএসসি, রাজ্য পিএসসি।

Latest Orthogonal Matrix MCQ Objective Questions

Orthogonal Matrix Question 1:

যদি A একটি 3 ক্রমের বর্গ ম্যাট্রিক্স হয় যেমন |A| = 3, তাহলে adj (adj A) হল:

27A
3A
9A
A

Answer (Detailed Solution Below)

Option 2 : 3A

ধারণা ব্যবহৃত:

A^{- 1} = \frac{adj A}{| A |} \Rightarrow adj A = | A | A^{- 1}

| k A | = k^{n} | A |, (k A)^{- 1} = \frac{1}{k} A^{- 1}

এবং

| A^{- 1} | = \frac{1}{| A |}

যেখানে k যেকোনো স্কেলার এবং n হল A-এর ক্রম।

গণনা:

adj (adj A) = | adj A | (adj A)^{- 1}

\Rightarrow | | A | A^{- 1} | {(| A | A^{- 1})}^{- 1} = | A |^{3} \cdot | A^{- 1} | \cdot \frac{1}{| A |} \cdot A

\Rightarrow | A |^{3 - 1 - 1} \cdot A = | A | A = 3 A

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free

Trusted by 7.3 Crore+ Students

Orthogonal Matrix Question 2:

যদি $A = \frac{1}{3} [\begin{matrix} 1 & 2 & a \\ 2 & 1 & b \\ 2 & - 2 & c \end{matrix}]$ লম্ব হয়, তাহলে A^-1 হবে

$\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & - 2 & 1 \end{matrix}]$
$\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & 2 & 1 \end{matrix}]$
$\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 1 \\ 2 & - 2 & 1 \end{matrix}]$
$\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1 \end{matrix}]$

Answer (Detailed Solution Below)

Option 4 :

\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1 \end{matrix}]

ব্যাখ্যা:

যেহেতু A লম্ব, AA^T = I

$\Rightarrow \frac{1}{3} [\begin{matrix} 1 & 2 & a \\ 2 & 1 & b \\ 2 & - 2 & c \end{matrix}] \frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ a & b & c \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$

$\Rightarrow [\begin{matrix} 1 + 4 + a^{2} & 2 + 2 + a b & 2 - 4 + a c \\ 2 + 2 + a b & 4 + 1 + b^{2} & 4 - 2 + b c \\ 2 - 4 + a c & 4 - 2 + b c & 4 + 4 + c^{2} \end{matrix}] = [\begin{matrix} 9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9 \end{matrix}]$

5 + a² = 9 ⇒ a = ±2

5 + b² = 9 ⇒ b = ±2

8 + c² = 9 ⇒ c = ±1

ab = -4, bc = -2, ac = 2

⇒ a = 2, b = -2, c = 1

যেহেতু A লম্ব, A^-1 = A^T

$A = \frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1 \end{matrix}]$

$A^{- 1} = A^{T} = \frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1 \end{matrix}]$

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free

Trusted by 7.3 Crore+ Students

Top Orthogonal Matrix MCQ Objective Questions

Orthogonal Matrix Question 3

Download Solution PDF

যদি A একটি 3 ক্রমের বর্গ ম্যাট্রিক্স হয় যেমন |A| = 3, তাহলে adj (adj A) হল:

27A
3A
9A
A

Answer (Detailed Solution Below)

Option 2 : 3A

ধারণা ব্যবহৃত:

A^{- 1} = \frac{adj A}{| A |} \Rightarrow adj A = | A | A^{- 1}

| k A | = k^{n} | A |, (k A)^{- 1} = \frac{1}{k} A^{- 1}

এবং

| A^{- 1} | = \frac{1}{| A |}

যেখানে k যেকোনো স্কেলার এবং n হল A-এর ক্রম।

গণনা:

adj (adj A) = | adj A | (adj A)^{- 1}

\Rightarrow | | A | A^{- 1} | {(| A | A^{- 1})}^{- 1} = | A |^{3} \cdot | A^{- 1} | \cdot \frac{1}{| A |} \cdot A

\Rightarrow | A |^{3 - 1 - 1} \cdot A = | A | A = 3 A

Download Solution PDF

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free

Trusted by 7.3 Crore+ Students

Orthogonal Matrix Question 4:

যদি $A = \frac{1}{3} [\begin{matrix} 1 & 2 & a \\ 2 & 1 & b \\ 2 & - 2 & c \end{matrix}]$ লম্ব হয়, তাহলে A^-1 হবে

$\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & - 2 & 1 \end{matrix}]$
$\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & 2 & 1 \end{matrix}]$
$\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 1 \\ 2 & - 2 & 1 \end{matrix}]$
$\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1 \end{matrix}]$

Answer (Detailed Solution Below)

Option 4 :

\frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1 \end{matrix}]

ব্যাখ্যা:

যেহেতু A লম্ব, AA^T = I

$\Rightarrow \frac{1}{3} [\begin{matrix} 1 & 2 & a \\ 2 & 1 & b \\ 2 & - 2 & c \end{matrix}] \frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ a & b & c \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$

$\Rightarrow [\begin{matrix} 1 + 4 + a^{2} & 2 + 2 + a b & 2 - 4 + a c \\ 2 + 2 + a b & 4 + 1 + b^{2} & 4 - 2 + b c \\ 2 - 4 + a c & 4 - 2 + b c & 4 + 4 + c^{2} \end{matrix}] = [\begin{matrix} 9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9 \end{matrix}]$

5 + a² = 9 ⇒ a = ±2

5 + b² = 9 ⇒ b = ±2

8 + c² = 9 ⇒ c = ±1

ab = -4, bc = -2, ac = 2

⇒ a = 2, b = -2, c = 1

যেহেতু A লম্ব, A^-1 = A^T

$A = \frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1 \end{matrix}]$

$A^{- 1} = A^{T} = \frac{1}{3} [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1 \end{matrix}]$

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free

Trusted by 7.3 Crore+ Students

Orthogonal Matrix Question 5:

যদি A একটি 3 ক্রমের বর্গ ম্যাট্রিক্স হয় যেমন |A| = 3, তাহলে adj (adj A) হল:

27A
3A
9A
A

Answer (Detailed Solution Below)

Option 2 : 3A

ধারণা ব্যবহৃত:

A^{- 1} = \frac{adj A}{| A |} \Rightarrow adj A = | A | A^{- 1}

| k A | = k^{n} | A |, (k A)^{- 1} = \frac{1}{k} A^{- 1}

এবং

| A^{- 1} | = \frac{1}{| A |}

যেখানে k যেকোনো স্কেলার এবং n হল A-এর ক্রম।

গণনা:

adj (adj A) = | adj A | (adj A)^{- 1}

\Rightarrow | | A | A^{- 1} | {(| A | A^{- 1})}^{- 1} = | A |^{3} \cdot | A^{- 1} | \cdot \frac{1}{| A |} \cdot A

\Rightarrow | A |^{3 - 1 - 1} \cdot A = | A | A = 3 A

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free

Trusted by 7.3 Crore+ Students

Exams

Test Series

SuperCoaching

Previous Year Papers

Latest Updates

MCQ Questions

Testbook Products & Resources for Students

Testbook USA

Books

Orthogonal Matrix MCQ Quiz in বাংলা - Objective Question with Answer for Orthogonal Matrix - বিনামূল্যে ডাউনলোড করুন [PDF]

Latest Orthogonal Matrix MCQ Objective Questions

Orthogonal Matrix Question 1:

Answer (Detailed Solution Below)

Orthogonal Matrix Question 1 Detailed Solution

Orthogonal Matrix Question 2:

Answer (Detailed Solution Below)

Orthogonal Matrix Question 2 Detailed Solution

Top Orthogonal Matrix MCQ Objective Questions

Orthogonal Matrix Question 3

Answer (Detailed Solution Below)

Orthogonal Matrix Question 3 Detailed Solution

Orthogonal Matrix Question 4:

Answer (Detailed Solution Below)

Orthogonal Matrix Question 4 Detailed Solution

Orthogonal Matrix Question 5:

Answer (Detailed Solution Below)

Orthogonal Matrix Question 5 Detailed Solution

Exam Preparation
Simplified

Orthogonal Matrix MCQ Quiz in বাংলা - Objective Question with Answer for Orthogonal Matrix - বিনামূল্যে ডাউনলোড করুন [PDF]

Latest Orthogonal Matrix MCQ Objective Questions

Orthogonal Matrix Question 1:

Answer (Detailed Solution Below)

Orthogonal Matrix Question 1 Detailed Solution

Orthogonal Matrix Question 2:

Answer (Detailed Solution Below)

Orthogonal Matrix Question 2 Detailed Solution

Top Orthogonal Matrix MCQ Objective Questions

Orthogonal Matrix Question 3

Answer (Detailed Solution Below)

Orthogonal Matrix Question 3 Detailed Solution

Orthogonal Matrix Question 4:

Answer (Detailed Solution Below)

Orthogonal Matrix Question 4 Detailed Solution

Orthogonal Matrix Question 5:

Answer (Detailed Solution Below)

Orthogonal Matrix Question 5 Detailed Solution

Exam Preparation Simplified

Related MCQ

Exam Preparation
Simplified