Advertisements
Advertisements
Question
Choose the correct alternative:
Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?
Options
A + B is a symmetric matrix
AB is a symmetric matrix
AB = (BA)T
ATB = MIT
Solution
AB is a symmetric matrix
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 order of the matrix
If a matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?
Find the values of x, y and z from the following equation
`[(12, 3),(x, 3/2)] = [(y, z),(3, 5)]`
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + B = B + A
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + (– A) = (– A) + A = 0
If A = `[(5, 2, 9),(1, 2, 8)]`, B = `[(1, 7),(1, 2),(5, -1)]` verify that (AB)T = BT AT
If A = `[(3, 1),(-1, 2)]` show that A2 – 5A + 7I2 = 0
Given A = `[("p", 0),(0, 2)]`, B = `[(0, -"q"),(1, 0)]`, C = `[(2, -2),(2, 2)]` and if BA = C2, find p and q.
A = `[(3, 0),(4, 5)]`, B = `[(6, 3),(8, 5)]`, C = `[(3, 6),(1, 1)]` find the matrix D, such that CD – AB = 0
Give your own examples of matrices satisfying the following conditions:
A and B such that AB ≠ BA
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 = BA, A ≠ 0 and B ≠ 0
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 and BA ≠ 0
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(A – B)T = AT – BT
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(BT)T = B
Choose the correct alternative:
If A and B are two matrices such that A + B and AB are both defined, then
Choose the correct alternative:
The matrix A satisfying the equation `[(1, 3),(0, 1)] "A" = [(1, 1),(0, -1)]` is
Choose the correct alternative:
If A + I = `[(3, -2),(4, 1)]`, then (A + I)(A – I) is equal to
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
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 ______.