Advertisements
Advertisements
Question
If `[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)]` is skew – symmetric find the values of p, q and r
Solution
Let A = `[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)]`
AT = `[(0, 2, "r"),("p", "q"^2, 1),(3, -1, 0)]`
A is skew-symmetric if A = – AT
`[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)] = - [(0, 2, "r"),("p", "q"^2, 1),(3, -1, 0)]`
`[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)] = [(0, -2, -"r"),(-"p", -"q"^2, -1),(-3, 1, 0)]`
Equating the corresponding entries.
p = – 2, r = – 3
q2 = – q2
⇒ q2 + q2 = 0
⇒ 2q2 = 0
⇒ q = 0
∴ The required values are
p = – 2, q = 0, r = – 3
APPEARS IN
RELATED QUESTIONS
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, Write the elements a22, a23, a24, a34, a43, a44
Construct a 3 × 3 matrix whose elements are given by aij = |i – 2j|
If A = `[(5, 4, 3),(1, -7, 9),(3, 8, 2)]` then find the transpose of A
If A = `[(4, 3, 1),(2, 3, -8),(1, 0, -4)]`, B = `[(2, 3, 4),(1, 9, 2),(-7, 1, -1)]` and C = `[(8, 3, 4),(1, -2, 3),(2, 4, -1)]` then verify that A + (B + C) = (A + B) + C
Find X and Y if X + Y = `[(7, 0),(3, 5)]` and X – Y = `[(3, 0),(0, 4)]`
Find the values of x, y, z if `[(x - 3, 3x - z),(x + y + 7, x + y + z)] = [(1, 0),(1, 6)]`
For the given matrix A = `[(1, 3, 5, 7),(2, 4, 6, 8),(9, 11, 13, 15)]` the order of the matrix AT is
If the number of columns and rows are not equal in a matrix then it is said to be a
Determine the value of x + y if `[(2x + y, 4x),(5x - 7, 4x)] = [(7, 7y - 13),(y, x + 6)]`
If A is a square matrix such that A2 = A, find the value of 7A – (I + A)3
Let A and B be two symmetric matrices. Prove that AB = BA if and only if AB is a symmetric matrix
Choose the correct alternative:
If A is a square matrix, then which of the following is not symmetric?
Choose the correct alternative:
If A and B are symmetric matrices of order n, where (A ≠ B), then
Let det M denotes the determinant of the matrix M. Let A and B be 3 × 3 matrices with det A = 3 and det B = 4. Then the det (2AB) is
If the matrix 'A' is both symmetric and strew symmetric then.
Let A = [aij] be a square matrix of order 3 such that aij = 2j – i, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + ... + A10 is equal to ______.
Let M = `[(0, -α),(α, 0)]`, where α is a non-zero real number an N = `sum_(k = 1)^49`M2k. If (I – M2)N = –2I, then the positive integral value of α is ______.
The total number of matrices formed with the help of 6 different numbers are ______.
