Advertisements
Advertisements
प्रश्न
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 = BA, A ≠ 0 and B ≠ 0
उत्तर
Let A = `[(x, - x),(-x, x)] ≠ 0`
B = `[(1, 1),(1, 1)] ≠ 0`
AB = `[(x, - x),(-x, x)] [(1, 1),(1, 1)]`
= `[(x - x, x - x),(-x + x, - x + x)]`
AB = `[(0, 0),(0, 0)]`
BA = `[(1, 1),(1, 1)] [(x, -x),(-x, x)]`
BA = `[(x - x, -x + x),(x - x, - x + x)]`
BA = `[(0, 0),(0, 0)]`
Martices A and B satisfies the condition
AB = 0 = BA
A ≠ 0
B ≠ 0.
APPEARS IN
संबंधित प्रश्न
If A = `[(sqrt(7), - 3),(- sqrt(5), 2),(sqrt(3), -5)]` then find the transpose of – A
If A = `[(5, 2, 2),(-sqrt(17), 0.7, 5/2),(8, 3, 1)]` then verify (AT)T = A
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?
If A = `[("a", "b"),("c", "d")]` and I = `[(1, 0),(0, 1)]` show that A2 – (a + d)A = (bc – ad)I2
If A = `[(3, 1),(-1, 2)]` show that A2 – 5A + 7I2 = 0
If A = `[(1, 2, 3),(3, 2, 1)]`, B = `[(1, 0),(2, -1),(0, 2)]` and C = `[(0, 1),(-2, 5)]` Which of the following statements are correct?
(i) AB + C = `[(5, 5),(5, 5)]`
(ii) BC = `[(0, 1),(2, -3),(-4, 10)]`
(iii) BA + C = `[(2, 5),(3, 0)]`
(iv) (AB)C = `[(-8, 20),(-8, 13)]`
Given A = `[("p", 0),(0, 2)]`, B = `[(0, -"q"),(1, 0)]`, C = `[(2, -2),(2, 2)]` and if BA = C2, find p and q.
Consider the matrix Aα = `[(cos alpha, - sin alpha),(sin alpha, cos alpha)]` Find all possible real values of α satisfying the condition `"A"_alpha + "A"_alpha^"T"` = I
If A = `[(1, 0, 2), (0, 2, 1), (2, 0, 3)]` and A3 – 6A2 + 7A + kI = 0, find the value of k
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(BT)T = B
If A is a 3 × 4 matrix and B is a matrix such that both ATB and BAT are defined, what is the order of the matrix B?
Choose the correct alternative:
If aij = (3i – 2j) and A = [aij]3 × 2 is
Choose the correct alternative:
What must be the matrix X, if `2"X" + [(1, 2),(3, 4)] = [(3, 8),(7, 2)]`?
Choose the correct alternative:
if A = `[(lambda, 1),(-1, -lambda)]`, then for what value of λ, A2 = 0 ?
Choose the correct alternative:
If a ≠ b, b, c satisfy `|("a", 2"b", 2"c"),(3, "b", "c"),(4, "a", "b")|` = 0, then abc =
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 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 ______.
Let A = `((1, -1, 0),(0, 1, -1),(0, 0, 1))` and B = 7A20 – 20A7 + 2I, where I is an identity matrix of order 3 × 3. If B = [bij], then b13 is equal to ______.
