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RBSE Solutions for Class 12 Maths Chapter 3 आव्यूह Ex 3.2

May 4, 2019 by Fazal Leave a Comment

RBSE Solutions for Class 12 Maths Chapter 3 आव्यूह Ex 3.2 is part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths Chapter 3 आव्यूह Exercise 3.2.

Rajasthan Board RBSE Class 12 Maths Chapter 3 आव्यूह Ex 3.2

प्रश्न 1.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 1
हों, तो A + B व A – B ज्ञात कीजिए।
हल :
दिया है,
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 2
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 3

प्रश्न 2.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 4
हों, तो आव्यूह A व B ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 5

प्रश्न 3.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 6
हों, तो आव्यूह C ज्ञात कीजिए, जहाँ A + 2B + C = 0 तथा O शून्य आव्यूह है।
हल :
दिया है,
A + 2B + C = 0
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 7
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 8

प्रश्न 4.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 9
हों, तो 3A² – 2B ज्ञात कीजिए।
हुल :
प्रश्नानुसार,
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 10

प्रश्न 5.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 11
हो, तो दिखाओ कि AB ≠ BA.
हल :
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 12
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 13
समीकरण (i) और (ii) से स्पष्ट है :
AB ≠ BA.
इति सिद्धम्।

प्रश्न 6.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 14
तो प्रदर्शित कीजिए – f(A) f(B) = f(A + B).
हल :
दिया है,
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 15
तो सिद्ध करना है।
f(A) + f(B) = f(A + B)
L.H.S.= f(A) x f(B)
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 16

= f(A + B)
= R.H.S
इति सिद्धम्।

प्रश्न 7.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 17
हो, तो सिद्ध कीजिए : (AB)T = BTAT
हल :
दिया है,
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 18
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 19
समीकरण (i) और (iv) से
(AB)T = BTAT
इति सिद्धम्।

प्रश्न 8.
सिद्ध कीजिए :
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 20
हल :
दिया है,
LHS
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 21
= [ax + hy + gz hx + by + fz gx + fy + cz] \(\left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] \)
= (ax + hy + gz)x + (hx + by + fz) + (gx + fy + cz)z
= ax² + hxy + gzx + hxy + by² + fyz + gzx + fyz + cz²
= ax² + by² + cz² + 2hxy + 2fyz + 2gzx
= R.H.S.
इति सिद्धम्।

प्रश्न 9.
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 22
हल :
दिया है,
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 23
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 24
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 25

प्रश्न 10.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 26
जहाँ 0 शून्य आव्यूह है, तो a का मान ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 27
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 28
⇒2a² + 10a + 12 = 0
⇒a² + 50 + 6 = 0
⇒a² + 2a + 3a + b = 0
⇒a(a + 2) + 3(a + 2) = 0
⇒(a + 2) (a + 3) = 0
⇒a + 2 = 0, a + 3 = 0
⇒a = – 2, a = – 3
अत: a = -2, – 3.

प्रश्न 11.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 29
तथा (A + B)² = A² + B² हो, तो a व b के मान ज्ञात कीजिए।
हल :
दिया है,
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 30
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 31
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 32
संगत पदों की तुलना करने पर
⇒a² + 2a + 1 = a² + b – 1
⇒2a = b – 2 = 4 – 2 = 2
⇒a = 1, b = 4.

प्रश्न 12.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 33
हल:
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 34
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 35

प्रश्न 13.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 36
हो, तो K का मान ज्ञात कीजिए, जहाँ A² = 8A + KI
हल :
दिया है, A² = 8A + KI
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 37
दोनों पक्षों में a11 की तुलना करने पर।
⇒ 8 + k = 1 ⇒ k = 1 – 8 = – 7

प्रश्न 14.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 38
हो, तो A का मान ज्ञात कीजिए|
हल :
माना आव्यूह
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 39
2a11 – a21 = -2 ⇒ 2 x 1 – a21 = -2 ⇒ a21 = 4
2a12 – a22 = – 10 ⇒ 2(-4) – a22 = -10 ⇒ a22 = 2
2a13 – a23 = 6 ⇒ 2(3) – a23 = 6 ⇒ a23 = 0
अत: आव्यूह
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 40

प्रश्न 15.
यदि
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 41
हल :
दिया है,
RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 42 RBSE Solutions for Class 12 Maths Chapter 3 Ex 3.2 43

We hope the given RBSE Solutions for Class 12 Maths Chapter 3 आव्यूह Ex 3.2 will help you. If you have any query regarding RBSE Solutions for Class 12 Maths Chapter 3 आव्यूह Ex 3.2, drop a comment below and we will get back to you at the earliest.

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