Advertisements
Advertisements
Question
If A is of order p × q and B is of order q × r what is the order of AB and BA?
Solution
If A is of order p × q .....[∵ p × q q × r = p × r]
the order of AB = p × r .......[∵ q × r p × q = r ≠ p]
Product of BA cannot be defined/found as the number of columns in B ≠. The number of rows in A.
APPEARS IN
RELATED QUESTIONS
Find the values of x, y, z if `[(x), (y – z), (z + 3)] + [(y), (4), (3)] = [(4), (8), (16)]`
Given that A = `[(1, 3),(5, -1)]`, B = `[(1, -1, 2),(3, 5, 2)]`, C = `[(1, 3, 2),(-4, 1, 3)]` verify that A(B + C) = AB + AC
For the given matrix A = `[(1, 3, 5, 7),(2, 4, 6, 8),(9, 11, 13, 15)]` the order of the matrix AT is
Which of the following can be calculated from the given matrices A = `[(1, 2),(3, 4),(5, 6)]`, B = `[(1, 2, 3),(4, 5, 6),(7, 8, 9)]`,
(i) A2
(ii) B2
(iii) AB
(iv) BA
If `cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta[(x, -cos theta),(cos theta, x)]` = I2, find x.
Determine the value of x + y if `[(2x + y, 4x),(5x - 7, 4x)] = [(7, 7y - 13),(y, x + 6)]`
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 and BA ≠ 0
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(4, -2),(3, -5)]`
For what value of x, the matrix A = `[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)]` is skew – symmetric
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 ______.
