10th Maths Book Back Question and Answers – Chapter 3 Exercise 3.18:
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Samacheer Kalvi 10th Maths Book Back Answers – Ex 3.18 Algebra
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Chapter 3
Exercise 3.18 Algebra
1. If A is of order p × q and B is of order q × r what is the order of AB and BA?
Solution:
If A is of order p × q [∵ p × q q × r = p × r]
the order of AB = p × r [∵ q × r p × q = r ≠ p]
Product of BA cannot be defined/found as the number of columns in B ≠. The number of rows in A.
2. If A is of order p × q and B is of order q × r what is the order of AB and BA?
Answer:
Order of A = a × (a + 3)
Order of B = b × (17 – b)
Given: Product of AB exist
a + 3 = b
a – b = – 3 ….(1)
Product of BA exist
17 – b = a
– a – b = -17
a + b = 17 ………(2)
(1) + (2) ⇒ 2a = 14
a = 142 = 7
Substitute the value of a = 7 in (1)
7 – b = -3 ⇒ -b = -3 -7
-b = -10 ⇒ b = 10
The value of b = 7 and b = 10
3. Find the order of the product matrix AB if
Solution:
4.If A = [2453], B = [12−35] find AB, BA and check if AB = BA?
Solution:
5.
Solution:
6.Show that the matrices A = [1321], B = [1−3−21] satisfy commutative property AB = BA
Solution:
7.
(i) A(BC) = (AB)C
(ii) (A – B)C = (AC – BC)
(iii) (A- B)T = AT – BT
Solution:
(i) A(BC) = (AB)C
8.
Solution:
9.
10.Verify that A2 = I when A = (56−4−5)
Solution:
11.
12.
Solution:
13.If A = show that A2 – 5A + 7I2 = 0.
Solution:
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