RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.2 Solutions

  1. Compute the following sums: [[3, -2], [1, 4]]+[[-2, 4] [1, 3]] Watch Solution
  2. Compute the following sums: [[2, 1, 3], [0, 3, 5], [-1, 2, 5]] + [[1, -2, 3], [2, 6, 1], [0, -3, 1]] Watch Solution
  3. Let A=[[2, 4], [3, 2]], B=[[1, 3], [-2, 5]] and C=[[-2, 5], [3, 4]]. Find (i) 2A – 3B (ii) B – 4C (iii) 3A – C (iv) 3A – 2B + 3C Watch Solution
  4. If A=[[2, 3], [5, 7]], B=[[-1, 0, 2], [3, 4, 1]], C=[[-1, 2, 3], [2, 1, 0]], find (i) A+B and B+C (ii) 2B+3A and 3C-4B. Watch Solution
  5. Let A=[[-1, 0, 2], [3, 1, 4]], B=[[0, -2, 5], [1, -3, 1]] and C=[[1, -5, 2], [6, 0, -4]]. Compute 2A-3B+4C. Watch Solution
  6. If A = diag(2, -5, 9), B = diag(1, 1, -4) and C = diag(-6, 3, 4), find (i) A – 2B (ii) B+C-2A (iii) 2A + 3B – 5C Watch Solution
  7. Given the matrices A=[[2, 1, 1], [3, -1, 0], [0, 2, 4]], B=[[9, 7, -1], [3, 5, 4], [2, 1, 6]] and C=[[2, -4, 3], [1, -1, 0], [9, 4, 5]] Verify that (A+B)+C=A+(B+C). Watch Solution
  8. Find matrices X and Y, if X + Y=[[5, 2], [0, 9]] and X – Y=[[3, 6], [0, -1]]. Watch Solution
  9. Find X, if Y = [[3, 2], [1, 4]] and 2X + Y = [[1, 0], [-3, 2]] Watch Solution
  10. Find matrices X and Y, if 2X – Y = [[6, -6, 0], [-4, 2, 1]] and X + 2Y = [[3, 2, 5], [-2, 1, -7]] Watch Solution
  11. If X – Y = [[1, 1, 1],[1, 1, 0],[1, 0, 0]] and X + Y = [[3, 5, 1],[-1, 1, 4],[11, 8, 0]], find X and Y. Watch Solution
  12. Find matrix A, if [[1, 2, -1], [0, 4, 9]] + A = [[9, -1, 4], [-2, 1, 3]] Watch Solution
  13. If A=[[9, 1], [7, 8]], B=[[1, 5], [7, 12]], find matrix C such that 5A + 3B + 2C is a null matrix. Watch Solution
  14. If A=[[2, -2], [4, 2], [-5, 1]], B=[[8, 0], [4, -2], [3, 6]], find matrix X such that 2A + 3X = 5B. Watch Solution
  15. If A=[[1, -3, 2], [2, 0, 2]] and B = [[2, -1, -1], [1, 0, -1]], find the matrix C such that A+B+C is zero matrix. Watch Solution
  16. Find x, y satisfying the matrix equations. [[x-y, 2, -2], [4, x, 6]] + [[3, -2, 2], [1, 0, -1]] = [[6, 0, 0], [5, 2x+y, 5]] Watch Solution
  17. Find x, y satisfying the matrix equations. [x, y+2, z-3] + [y, 4, 5] = [4, 9, 12] Watch Solution
  18. Find x, y satisfying the matrix equations. x[[2], [1]] + y[[3], [5]] + [[-8],[11]] = O Watch Solution
  19. If 2[[3, 4], [5, x]]+[[1, y], [0, 1]]=[[7, 0], [10, 5]]. find x and y. Watch Solution
  20. Find the value of λ., a non-zero scalar, if λ.[[1, 0, 2], [3, 4, 5]] + 2[[1, 2, 3], [-1, -3, 2]=[[4, 4, 10], [4, 2, 14]] Watch Solution
  21. Find a matrix X such that 2A + B + X = 0, where A = [[-1, 2], [3, 4]], B = [[3, -2], [1, 5]] Watch Solution
  22. If A=[[8, 0], [4, -2], [3, 6]] and B=[[2, -2], [4, 2], [-5, 1]], then find the matrix X of order 3×2 such that 2A + 3X = 5B. Watch Solution
  23. Find x, y, z and t, if 3[[x, y], [z, t]] = [[x, 6], [-1, 2t], [[4, x + y], [z + t, 3]] Watch Solution
  24. Find x, y, z and t if 2[[x, 5], [7, y-3]]+[[3, 4], [1, 2]] = [[7, 14], [15, 14]] Watch Solution
  25. If X and Y are 2×2 matrices, then solve the following matrix equations for X and Y. 2X + 3Y=[[2, 3], [4, 0]], 3X + 2Y = [[-2, 2], [1, -5]] Watch Solution
  26. In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges. Watch Solution
  27. The monthly incomes of Aryan and Babban are in the ratio 3:4 and their monthly expenditures are in the ratio 5:7. If each saves ₹15000 per month, find their monthly income using matrix method. This problem reflects which value? 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

 

 

 

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