10th Maths - Book Back Answers - Chapter 3 Exercise 3.19 - English Medium Guides

  

 

SSLC / 10th - Maths - Book Back Answers - Chapter 3 Exercise 3.19 - English Medium

Tamil Nadu Board 10th Standard Maths - Chapter 3 Exercise 3.19: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 3 Exercise 3.19 – Maths from the Tamil Nadu State Board 10th Standard textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 3 Exercise 3.19 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 10 students! Prepare well and aim for top scores. Thank you!

Chapter 3 Algebra Ex 3.19

1.  Find the order of the product matrix AB if

	(i)	(ii)	(iii)	(iv)	(v)
Orders of A	3×3	4×3	4×2	4×5	1×1
Orders of A	3×3	3×2	2×2	5×1	1×3

Answer Key:
Given A = [a_ij]_p×q and B = [a_ij]_q×r
Order of product of AB = p × r
Order of product of BA is not defined. Number columns in r is not equal to the number of rows in P.

∴ Product BA is not defined.

 

2. A has ‘a’ rows and ‘a + 3 ’ columns. B has ‘6’ rows and ‘17 – b’ columns, and if both products AB and BA exist, find a, b?
Answer Key:
 A has a rows, a + 3 columns.
B has b rows, 17 – b columns

If AB exists a × a + 3
b × 17 – b
a + 3 = 6 ⇒ a – 6 = -3 ………… (1)
If BA exists 6 × 17-6
a × a + 3
17 – 6 = a ⇒ a + 6 = 17 …………. (2)
(1) + (2) ⇒ 2a = 14 ⇒ a = 7
Substitute a = 7 in (1) ⇒ 7 – b = -3 ⇒ b = 10
a = 7, b = 10

 

3. A has ‘a’ rows and ‘a + 3 ’ columns. B has rows and ‘b’ columns, and if both products AB and BA exist, find a,b?
Answer Key:

1. Order of matrix AB = 3 × 3
2. Order of matrix AB = 4 × 2
3. Order of matrix AB = 4 × 2
4. Order of matrix AB = 4 × 1
5. Order of matrix AB = 1 × 3

 

4.

find AB, BA and check if AB = BA?
Answer Key:

5. Given that

verify that A(B + C) = AB + AC
Answer Key:

From (1) and (2) we get
A (B + C) = AB + AC

 

6. Show that the matrices

satisfy commutative property AB = BA
Answer Key:

From (1) and (2) we get
AB = BA. It satisfy the commutative property.

 

7. 

Show that (i) A(BC) = (AB)C
(ii) (A-B)C = AC – BC
(iii) (A-B)^T = A^T – B^T
Answer Key:

 From (1) and (2) we get
A(BC) = (AB)C

From (1) and (2) we get
(A – B) C = AC – BC 

From (1) and (2) we get
(A-B)^T = A^T – B^T

 

8. 

then snow that A² + B² = I.
Answer Key:

 

9. 

prove that AA^T = I.

Answer Key:

AA^T = I
∴ L.H.S. = R.H.S.

 

10. 

Verify that A² = I when

Answer Key:

∴ L.H.S. = R.H.S.

 

11. 

show that A² – (a + d)A = (bc – ad)I₂.
Answer Key:

L.H.S. = R.H.S.
A² – (a + d) A = (bc – ad)I₂

 

12. 

verify that (AB)^T = B^T A^T
Answer Key:

From (1) and (2) we get, (AB)^T = B^T A^T

 

13. 

show that A² – 5A + 7I₂ = 0
Answer Key:

L.H.S. = R.H.S.
∴ A² – 5A + 7I₂ = 0