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. If A = [[-2], [4], [5]], B = [1, 3, -6], verify that (AB)^T = B^TA^T Watch Solution
8. If A=[[2, 4, -1], [-1, 0, 2]], B=[[3, 4], [-1, 2], [2, 1]], find (AB)^T Watch Solution
9. 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
10. 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
11. If A^T = [[3, 4], [-1, 2], [0, 1]] and B = [[-1, 2, 1], [1, 2, 3]], find A^T – B^T Watch Solution
12. If A = [[cos α, sin α], [-sin α, cos α]], then verify that A^T A = I2. Watch Solution
13. If A = [[sin α, cos α], [-cos α, sin α]], verify that A^T A = I2 Watch Solution
14. 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