RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.5 Solutions If A=[[2, 3], [4, 5]], prove that A – A^T is skew-symmetric matrix. Watch Solution If A = [[3, -4], [1, -1]], show that A – A^T is a skew-symmetric matrix. Watch Solution If the matrix A = [[5, 2, x], [y, z, -3], [4, […]
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.4 Solutions Let A = [[2, -3],[-7, 5]] and B=[[1, 0],[2, -4]], verify that (2A)^T = 2A^T Watch Solution Let A = [[2, -3], [-7, 5]] and B = [[1, 0], [2, -4]], verify that (A + B)^T = A^T + B^T Watch Solution Let A =
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.3 Solutions Compute the indicated product : [[a, b], [-b, a]] [[a, -b], [b, a]] Watch Solution Compute the indicated product : [[1, -2], [2, 3]] [[1, 2, 3], [-3, 2, -1]] Watch Solution Compute the indicated product : [[2, 3, 4], [3, 4, 5], [4, 5,
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.2 Solutions Compute the following sums: [[3, -2], [1, 4]]+[[-2, 4] [1, 3]] Watch Solution Compute the following sums: [[2, 1, 3], [0, 3, 5], [-1, 2, 5]] + [[1, -2, 3], [2, 6, 1], [0, -3, 1]] Watch Solution Let A=[[2, 4], [3, 2]], B=[[1, 3],
RD Sharma Chapter 4 : Inverse Trigonometric Function Very Short Type Questions (VSAQs) Solutions Write the value of sin^-1(-√3/2) + cos^-1(-1/2) Watch Solution Write the difference between maximum and minimum values of sin^-1x for x ∈[-1,1] Watch Solution If sin^-1x+sin^-1y + sin^-1z = 3π/2, then write the value of x + y + z. Watch Solution
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.1 Solutions If a matrix has 8 elements, what are the possible orders it can have ? What if it has 5 elements ? Watch Solution If A = [aij] = [[2,3,-5],[1,4,9],[0,7,-2]] and B = [bij] = [[2,-1],[-3,4],[1,2]] then find (i) a22 + b21 (ii) a11b11 +
RD Sharma Chapter 4 : Inverse Trigonometric Function Multiple Choice Questions (MCQs) Solutions If tan^-1{(√1+x^2)-(√1-x^2)/(√1+x^2)+(√1-x^2)} = α, then x^2= Watch Solution The value of tan{cos^-1(1/5√2) – sin^-1(4/17)} is Watch Solution 2tan^-1{cosec(tan^-1x) – tan(cot^-1x)} is equal to Watch Solution If cos^-1(x/a) + cos^-1(y/b) = α, then x^2/a^2 – (2xy/ab)cosα + y^2/b^2 = Watch Solution The positive integral
RD Sharma Chapter 4 : Inverse Trigonometric Function Exercise 4.14 Solutions Prove the result : 2sin^-1(3/5) = tan^-1(24/7) Watch Solution Evaluate : tan{2tan^-1(1/5)-π/4} Watch Solution Evaluate : tan(1/2sin^-1(3/4)) Watch Solution Evaluate : sin(1/2cos^-1(4/5)) Watch Solution Evaluate : sin(2tan^-1(2/3)) + cos(tan^-1√3) Watch Solution Prove the result : tan^-1(1/4) + tan^-1(2/9) = (1/2)cos^-1(3/5) = (1/2)sin^-1(4/5) Watch Solution Prove
RD Sharma Chapter 4 : Inverse Trigonometric Function Exercise 4.13 Solutions If cos^-1(x/2) + cos^-1(y/3) = α, then prove that 9x^2 – 12xycos α + 4y^2 = 36sin^2 α. Watch Solution Solve the equation : cos^-1(a/x) – cos^-1(b/x) = cos^-1(1/b) – cos^-1(1/a) Watch Solution Solve cos^-1(√3x) + cos^-1(x) = π/2 Watch Solution Prove that: cos^-1(4/5) +
RD Sharma Chapter 4 : Inverse Trigonometric Function Exercise 4.12 Solution Evaluate : cos(sin^-1(3/5) + sin^-1(5/13)) Watch Solution Prove the result : sin^-1(63/65) = sin^-1(5/13) + cos^-1(3/5) Watch Solution Prove the result : sin^-1(5/13) + cos^-1(3/5) = tan^-1(63/16) Watch Solution Prove the result : (9π/8) – (9/4)sin^-1 (1/3) = (9/4)sin^-1(2√2/3) Watch Solution Solve : sin^-1(x) +