Advertisements
Advertisements
Question
Give your own examples of matrices satisfying the following conditions:
A and B such that AB ≠ BA
Solution
Let A = `[(1, 2),(4, 5)]` and B = `[(3, 1),(5, 2)]`
AB = `[(1, 2),(4, 5)] [(3, 1),(5, 2)]`
=`[(3 + 10, 1 + 4),(12 + 25, 4 + 10)]`
AB = `[(13, 5),(37, 14)]` ......(1)
BA = `[(3, 1),(5, 2)] [(1, 2),(4, 5)]`
= `[(3 + 4, 6 + 5),(5 + 8, 10 + 10)]`
BA = `[(7, 11),(13, 20)]` ......(2)
From equation (1) and (2)
AB ≠ BA
APPEARS IN
RELATED QUESTIONS
If A = `[(5, 4, 3),(1, -7, 9),(3, 8, 2)]` then find the transpose of A
Find the values of x, y and z from the following equation
`[(12, 3),(x, 3/2)] = [(y, z),(3, 5)]`
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of 3A – 9B
Find x and y if `x[(4),(-3)] + y[(-2),(3)] = [(4),(6)]`
If A = `[(2, 5),(4, 3)]`, B = `[(1, -3),(2, 5)]` find AB, BA and verify AB = BA?
If A = `[("a", "b"),("c", "d")]` and I = `[(1, 0),(0, 1)]` show that A2 – (a + d)A = (bc – ad)I2
If `cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta[(x, -cos theta),(cos theta, x)]` = I2, find x.
A = `[(3, 0),(4, 5)]`, B = `[(6, 3),(8, 5)]`, C = `[(3, 6),(1, 1)]` find the matrix D, such that CD – AB = 0
If A = `[(1, 0, 0),(0, 1, 0),("a", "b", - 1)]`, show that A2 is a unit matrix
If A is a square matrix such that A2 = A, find the value of 7A – (I + A)3
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(4, -2),(3, -5)]`
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:
if A = `[(lambda, 1),(-1, -lambda)]`, then for what value of λ, A2 = 0 ?
Choose the correct alternative:
If the points (x, – 2), (5, 2), (8, 8) are collinear, then x is equal to
Choose the correct alternative:
If the square of the matrix `[(alpha, beta),(γ, - alpha)]` is the unit matrix of order 2, then α, β, and γ should
Choose the correct alternative:
If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC is
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?
Let P = `[(3, -1, -2),(2, 0, alpha),(3, -5, 0)]`, where α ∈ R. Suppose Q = [qij] is a matrix satisfying PQ = kI3 for some non-zero k ∈ R. If q23 = `-k/8` and |Q| = `k^2/2`, then α2 + k2 is equal to ______.
Let A = `[(cosα, -sinα),(sinα, cosα)]`, α ∈ R such that A32 = `[(0, -1),(1, 0)]`. Then a value of α is ______.
The number of matrices A = `[(a, b),(c, d)]`, where a, b, c, d ∈ {–1, 0, 1, 2, 3, ............, 10} such that A = A–1, is ______.
