Advertisements
Advertisements
प्रश्न
A has ‘a’ rows and ‘a + 3’ columns. B has ‘b’ rows and ‘17 − b’ columns, and if both products AB and BA exist, find a, b?
उत्तर
Order of A = a × (a + 3)
Order of B = b × (17 – b)
Given: Product of AB exist
a + 3 = b
a – b = – 3 ….(1)
Product of BA exist
17 – b = a
– a – b = – 17
a + b = 17 ………(2)
(1) + (2) ⇒ 2a = 14
a = `14/2` = 7
Substitute the value of a = 7 in (1)
7 – b = – 3 ⇒ – b = – 3 – 7
– b = – 10 ⇒ b = 10
The value of a = 7 and b = 10
APPEARS IN
संबंधित प्रश्न
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
Find the values of x, y and z from the following equation
`[(x + y, 2),(5 + z, xy)] = [(6, 2),(5, 8)]`
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + B = B + A
Solve for x, y : `[(x^2),(y^2)] + 2[(-2x),(-y)] = [(5),(8)]`
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 AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(BT)T = B
If A and B are symmetric matrices of same order, prove that AB – BA is a skew-symmetric matrix
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
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 ______.
