Class 12 Maths – RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.4 Solutions (Step-by-Step Guide)

RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.4 Solutions

1. Let A = [[2, -3],[-7, 5]] and B=[[1, 0],[2, -4]], verify that (2A)^T = 2A^T Watch Solution
2. Let A = [[2, -3], [-7, 5]] and B = [[1, 0], [2, -4]], verify that (A + B)^T = A^T + B^T Watch Solution
3. Let A = [[2, -3],[-7, 5]] and B=[[1, 0],[2, -4]], verify that (A – B)^T = A^T – B^T Watch Solution
4. Let A = [[2, -3],[-7, 5]] and B = [[1, 0],[2, -4]], verify that (AB)^T = B^TA^T Watch Solution
5. If A = [[3], [5], [2]] and B = [1, 0, 4], verify that (AB)^T = B^TA^T. Watch Solution
6. Let A = [[1, -1, 0], [2, 1, 3], [1, 2, 1]] and B = [[1, 2, 3], [2, 1, 3], [0, 1, 1]]. Find A^T, B^T and verify that (i) (A + B)^T = A^T + B^T (ii) (AB)^T = B^TA^T (iii) (2A)^T = 2A^T Watch Solution
7. Let A = [[1, -1, 0], [2, 1, 3], [1, 2, 1]] and B = [[1, 2, 3], [2, 1, 3], [0, 1, 1]]. Find A^T, B^T and verify that (A + B)^T = A^T + B^T Watch Solution
8. Let A = [[1, -1, 0], [2, 1, 3], [1, 2, 1]] and B = [[1, 2, 3], [2, 1, 3], [0, 1, 1]]. Verify that (AB)^T = B^T A^T Watch Solution
9. Let A = [[1, -1, 0], [2, 1, 3], [1, 2, 1]] and B = [[1, 2, 3], [2, 1, 3], [0, 1, 1]]. Verify that (2A)^T = 2A^T Watch Solution
10. If A = [[-2], [4], [5]], B = [1, 3, -6], verify that (AB)^T = B^TA^T Watch Solution
11. If A=[[2, 4, -1], [-1, 0, 2]], B=[[3, 4], [-1, 2], [2, 1]], find (AB)^T Watch Solution
12. For two matrices A and B, A = [[2, 1, 3], [4, 1, 0]], B = [[1, -1], [0, 2], [5, 0]] verify that (AB)^T = B^TA^T Watch Solution
13. For the matrices, A and B, verify that (AB)^T = B^TA^T, where A = [[1, 3], [2, 4]], B = [[1, 4], [2, 5]] Watch Solution
14. If A^T = [[3, 4], [-1, 2], [0, 1]] and B = [[-1, 2, 1], [1, 2, 3]], find A^T – B^T Watch Solution
15. If A = [[cos α, sin α], [-sin α, cos α]], then verify that A^T A = I2. Watch Solution
16. If A = [[sin α, cos α], [-cos α, sin α]], verify that A^T A = I2 Watch Solution
17. If l1, m1, n1 ; i=1,2,3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AA^T = I, where A=[[l1, m1, m1], [l2, m2, n2], [l3, m3, n3]] Watch Solution

 

ALGEBRA OF MATRICES – R.D. Sharma Class 12th Math

1. Algebra of Matrices Exercise 5.1 Video Solution
2. Algebra of Matrices Exercise 5.2 Video Solution
3. Algebra of Matrices Exercise 5.3 Video Solution
4. Algebra of Matrices Exercise 5.4 Video Solution
5. Algebra of Matrices Exercise 5.5 Video Solution
6. Algebra of Matrices Very Short Answer Questions (VSAQs) Video Solution
7. Algebra of Matrices Multiple Choice Questions (MCQs) Video Solution