RD Sharma Solutions for Class 12 Maths Exercise 5.4 Chapter 5 Algebra of Matrices is provided here for students to study and score good marks in the board exams. In order to excel in the CBSE exam for Class 12, students can use the solutions of Exercise 5.4 available on the website. By practising regularly the students can obtain worthy results in the Class 12 exams by using the RD Sharma Solutions.
The PDF of RD Sharma Solutions of exercise 5.4 primarily helps students from the exam point of view. This exercise mainly contains solved problems based on the concept of symmetric and skew-symmetric matrices. RD Sharma Solutions for Class 12 Maths Chapter 5 Algebra of Matrices Exercise 5.4 are provided here.
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(i) (2A)T = 2 AT
(ii) (A + B)T = AT + BT
(iii) (A – B)T = AT – BT
(iv) (AB)T = BT AT
Solution:
(i) Given
Consider,
Put the value of A
L.H.S = R.H.S
(ii) Given
Consider,
L.H.S = R.H.S
Hence proved.
(iii) Given
Consider,
L.H.S = R.H.S
(iv) Given
So,
Solution:
Given
L.H.S = R.H.S
So,
(i) A + B)T = AT + BT
(ii) (AB)T = BT AT
(iii) (2A)T = 2 AT
Solution:
(i) Given
Consider,
L.H.S = R.H.S
So,
(ii) Given
Consider,
L.H.S = R.H.S
So,
(iii) Given
Consider,
L.H.S = R.H.S
So,
Solution:
Given
Consider,
L.H.S = R.H.S
So,
Solution:
Given
Now we have to find (AB)T
So,